Abstract group data - 6912.ia

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 4, 6, 6, 12, 12, 12], 'aut_gens': [[7620480, 127370880, 43548276, 80205945, 87178291200, 47537280, 6274228129, 174356582400, 174400491626, 93532719813, 40279680], [39953733, 87091200, 83839371, 119783329, 87178328133, 47537280, 180627522425, 93405312000, 93492787129, 174443710533, 127370880], [83462400, 127370880, 120127371, 47183865, 180583640133, 79833600, 6307235148, 93405312000, 93525068087, 174483990213, 40279680], [123742080, 40279680, 7264451, 127025868, 6227057733, 47537280, 180671068025, 174356582400, 174403783669, 93445628613, 87091200], [3665733, 40279680, 83832131, 127017465, 87178291200, 79833600, 6314498324, 174356582400, 174436793367, 93445628613, 87091200], [3628800, 40279680, 120144463, 87483364, 87178291200, 3991680, 6354061729, 174356582400, 174436794856, 93445628613, 87091200], [123742080, 40279680, 7288783, 127031444, 87178291200, 47537280, 180671066745, 93405312000, 93452518246, 174396899013, 87091200], [83499333, 40279680, 4007407, 87471948, 6227020800, 43545600, 180710644129, 174356582400, 174400506856, 93445628613, 127370880]], 'aut_group': None, 'aut_hash': 3573172111550600594, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 27648, 'aut_permdeg': 30, 'aut_perms': [196574670567864430508783501430586, 40877630628039085319222822978450, 133434976328591841519997874192435, 146011444027425158868110239209139, 230397002173369809074358406742109, 133788664134100294958618438698383, 85880023044415839676471921604948], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 2, 1], [2, 9, 2, 1], [2, 12, 1, 1], [2, 18, 2, 1], [2, 36, 1, 2], [2, 72, 1, 1], [2, 108, 1, 1], [2, 216, 1, 1], [3, 2, 1, 1], [3, 8, 1, 2], [3, 16, 1, 2], [3, 64, 1, 1], [3, 128, 1, 1], [4, 6, 1, 1], [4, 6, 2, 1], [4, 18, 1, 2], [4, 18, 2, 1], [4, 36, 1, 2], [4, 54, 1, 1], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 2], [6, 12, 2, 1], [6, 16, 1, 2], [6, 24, 1, 3], [6, 24, 2, 2], [6, 48, 1, 2], [6, 48, 2, 1], [6, 64, 1, 1], [6, 72, 1, 1], [6, 72, 2, 1], [6, 96, 1, 1], [6, 96, 2, 1], [6, 128, 1, 1], [6, 144, 1, 1], [6, 144, 2, 1], [6, 192, 1, 1], [6, 192, 2, 1], [6, 288, 1, 1], [8, 6, 2, 1], [8, 18, 2, 2], [8, 36, 2, 2], [8, 54, 2, 1], [8, 108, 2, 2], [12, 12, 1, 1], [12, 12, 2, 1], [12, 36, 1, 1], [12, 48, 1, 1], [12, 48, 2, 1], [12, 72, 1, 2], [12, 96, 1, 1], [12, 96, 2, 1], [12, 144, 1, 2], [12, 144, 2, 1], [24, 12, 2, 1], [24, 36, 2, 1], [24, 48, 2, 1], [24, 72, 2, 2], [24, 96, 2, 1], [24, 144, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3\\times A_4^2.C_2^2\\times S_3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '3456.jo', 'autcentquo_hash': 2520327345672601111, 'autcentquo_nilpotent': False, 'autcentquo_order': 3456, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 4], [2, 6, 2], [2, 9, 2], [2, 12, 1], [2, 18, 2], [2, 36, 2], [2, 72, 1], [2, 108, 1], [2, 216, 1], [3, 2, 1], [3, 8, 2], [3, 16, 2], [3, 64, 1], [3, 128, 1], [4, 6, 3], [4, 18, 4], [4, 36, 2], [4, 54, 1], [4, 72, 1], [4, 108, 2], [4, 216, 1], [6, 2, 1], [6, 6, 2], [6, 8, 2], [6, 12, 2], [6, 16, 2], [6, 24, 7], [6, 48, 4], [6, 64, 1], [6, 72, 3], [6, 96, 3], [6, 128, 1], [6, 144, 3], [6, 192, 3], [6, 288, 1], [8, 6, 2], [8, 18, 4], [8, 36, 4], [8, 54, 2], [8, 108, 4], [12, 12, 3], [12, 36, 1], [12, 48, 3], [12, 72, 2], [12, 96, 3], [12, 144, 4], [24, 12, 2], [24, 36, 2], [24, 48, 2], [24, 72, 4], [24, 96, 2], [24, 144, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '3456.jo', 'commutator_count': 1, 'commutator_label': '864.4195', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 209, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['48.29', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 6, 1, 2], [2, 9, 1, 2], [2, 12, 1, 1], [2, 18, 1, 2], [2, 36, 1, 2], [2, 72, 1, 1], [2, 108, 1, 1], [2, 216, 1, 1], [3, 2, 1, 1], [3, 8, 1, 2], [3, 16, 1, 2], [3, 64, 1, 1], [3, 128, 1, 1], [4, 6, 1, 3], [4, 18, 1, 4], [4, 36, 1, 2], [4, 54, 1, 1], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 2], [6, 12, 1, 2], [6, 16, 1, 2], [6, 24, 1, 7], [6, 48, 1, 4], [6, 64, 1, 1], [6, 72, 1, 3], [6, 96, 1, 3], [6, 128, 1, 1], [6, 144, 1, 3], [6, 192, 1, 3], [6, 288, 1, 1], [8, 6, 2, 1], [8, 18, 2, 2], [8, 36, 2, 2], [8, 54, 2, 1], [8, 108, 2, 2], [12, 12, 1, 3], [12, 36, 1, 1], [12, 48, 1, 3], [12, 72, 1, 2], [12, 96, 1, 3], [12, 144, 1, 4], [24, 12, 2, 1], [24, 36, 2, 1], [24, 48, 2, 1], [24, 72, 2, 2], [24, 96, 2, 1], [24, 144, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 2419200, 'exponent': 24, 'exponents_of_order': [8, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [24, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '3456.jo', 'hash': 4930085545709402789, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 3, 4, 2, 3, 4, 3, 12, 6, 2], 'inner_gens': [[7620480, 40279680, 123381876, 87463545, 87178291200, 120113280, 6354061729, 174356582400, 174476333546, 93445628613, 127370880], [83462400, 127370880, 7260276, 80205945, 87178291200, 123379200, 6274228129, 174356582400, 174476333546, 93532719813, 40279680], [362880, 87091200, 43548276, 119773844, 87178291200, 3991680, 6270947148, 174356582400, 174483592212, 93492440133, 127370880], [39916800, 127370880, 123405310, 80205945, 87178291200, 43545600, 6274218644, 174356582400, 174483626639, 93532719813, 87091200], [7620480, 127370880, 43548276, 80205945, 87178291200, 47537280, 180630810529, 93405312000, 93449221226, 174483990213, 40279680], [123742080, 40279680, 7260276, 127017465, 87178291200, 47537280, 6314507809, 174356582400, 174403757546, 93445628613, 87091200], [362880, 127370880, 47544131, 80207225, 180583603200, 7257600, 6274228129, 93405312000, 93492780567, 174483990213, 87091200], [7620480, 127370880, 43548276, 80205945, 180583603200, 47537280, 87225498529, 174356582400, 174400491626, 93532719813, 40279680], [83462400, 40279680, 3994874, 87464825, 180583603200, 43545600, 87305328484, 174356582400, 174400491626, 93445628613, 127370880], [83462400, 127370880, 7260276, 80205945, 6227020800, 123379200, 180630810529, 174356582400, 174476333546, 93532719813, 40279680], [83462400, 127370880, 120115956, 47183865, 87178291200, 79833600, 6307250209, 174356582400, 174476333546, 93532719813, 40279680]], 'inner_hash': 2520327345672601111, 'inner_nilpotent': False, 'inner_order': 3456, 'inner_split': True, 'inner_tex': 'S_3\\times S_4^2', 'inner_used': [1, 2, 3, 4, 5, 7, 9], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 20], [3, 16], [4, 18], [6, 24], [8, 7], [9, 8], [12, 12], [16, 1], [18, 4], [24, 2]], 'label': '6912.ia', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'D6.S4^2', 'ngens': 11, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 87, 'number_characteristic_subgroups': 67, 'number_conjugacy_classes': 120, 'number_divisions': 105, 'number_normal_subgroups': 83, 'number_subgroup_autclasses': 3676, 'number_subgroup_classes': 4918, 'number_subgroups': 150202, 'old_label': None, 'order': 6912, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 559], [3, 242], [4, 720], [6, 2438], [8, 768], [12, 1224], [24, 960]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[7620480, 127370880, 43548276, 80205945, 87178328133, 47537280, 6274218644, 174356582400, 174400491626, 93532719813, 40279680], [7620480, 127370880, 43548276, 80205945, 87178291200, 47537280, 6274228129, 174356582400, 174400527119, 93532719813, 40279680], [7657413, 127370880, 43548276, 80207225, 87178291200, 47537280, 6274218644, 174356582400, 174400491626, 93532719813, 40279680]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 16], [4, 14], [6, 16], [8, 9], [9, 8], [12, 12], [16, 2], [18, 4], [24, 4]], 'representations': {'PC': {'code': '6187846104526929576604826054350833158790511891949585007462807337808917445735436437638288777550608838337972965665', 'gens': [1, 2, 4, 5, 7, 8, 9], 'pres': [11, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 51173, 56, 157478, 6867, 3446, 1609, 70965, 63881, 158, 3184, 479, 3031, 88722, 19059, 10094, 1140, 199603, 13120, 5409, 1471, 294, 26453, 328, 23286]}, 'Perm': {'d': 15, 'gens': [7620480, 127370880, 43548276, 80205945, 87178291200, 47537280, 6274228129, 174356582400, 174400491626, 93532719813, 40279680]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6.S_4^2', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 166693013
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 209, 'group_order': 6912, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 166693045
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 209, 'group_order': 6912, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 36933, 'size': 1}
  • id: 166693056
    {'aut_label': '2B', 'centralizer': '3.b1', 'counter': 3, 'group_counter': 209, 'group_order': 6912, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 40316613, 'size': 3}
  • id: 166693067
    {'aut_label': '2C', 'centralizer': '3.a1', 'counter': 4, 'group_counter': 209, 'group_order': 6912, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 6227020800, 'size': 3}
  • id: 166693078
    {'aut_label': '2C', 'centralizer': '3.a1', 'counter': 5, 'group_counter': 209, 'group_order': 6912, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 6227057733, 'size': 3}
  • id: 166693089
    {'aut_label': '2E', 'centralizer': '3.b1', 'counter': 6, 'group_counter': 209, 'group_order': 6912, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 87091200, 'size': 3}
  • id: 166693100
    {'aut_label': '2F', 'centralizer': '6.d1', 'counter': 7, 'group_counter': 209, 'group_order': 6912, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 362880, 'size': 6}
  • id: 166693111
    {'aut_label': '2F', 'centralizer': '6.d1', 'counter': 8, 'group_counter': 209, 'group_order': 6912, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 399813, 'size': 6}
  • id: 166693122
    {'aut_label': '2H', 'centralizer': '9.a1', 'counter': 9, 'group_counter': 209, 'group_order': 6912, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 6267300480, 'size': 9}
  • id: 166693014
    {'aut_label': '2H', 'centralizer': '9.a1', 'counter': 10, 'group_counter': 209, 'group_order': 6912, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 6267337413, 'size': 9}
  • id: 166693025
    {'aut_label': '2J', 'centralizer': '12.bo1', 'counter': 11, 'group_counter': 209, 'group_order': 6912, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 746, 'size': 12}
  • id: 166693036
    {'aut_label': '2K', 'centralizer': '18.a1', 'counter': 12, 'group_counter': 209, 'group_order': 6912, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 6227383680, 'size': 18}
  • id: 166693038
    {'aut_label': '2K', 'centralizer': '18.a1', 'counter': 13, 'group_counter': 209, 'group_order': 6912, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 180591260613, 'size': 18}
  • id: 166693039
    {'aut_label': '2M', 'centralizer': '36.gp1', 'counter': 14, 'group_counter': 209, 'group_order': 6912, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 40280426, 'size': 36}
  • id: 166693040
    {'aut_label': '2N', 'centralizer': '36.ge1', 'counter': 15, 'group_counter': 209, 'group_order': 6912, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 6227035287, 'size': 36}
  • id: 166693041
    {'aut_label': '2O', 'centralizer': '72.i1', 'counter': 16, 'group_counter': 209, 'group_order': 6912, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 7621226, 'size': 72}
  • id: 166693042
    {'aut_label': '2P', 'centralizer': '108.eu1', 'counter': 17, 'group_counter': 209, 'group_order': 6912, 'label': '2P', 'order': 2, 'powers': [1, 17], 'representative': 180711005926, 'size': 108}
  • id: 166693043
    {'aut_label': '2Q', 'centralizer': '216.b1', 'counter': 18, 'group_counter': 209, 'group_order': 6912, 'label': '2Q', 'order': 2, 'powers': [1, 18], 'representative': 180623521812, 'size': 216}
  • id: 166693044
    {'aut_label': '3A', 'centralizer': '2.d1', 'counter': 19, 'group_counter': 209, 'group_order': 6912, 'label': '3A', 'order': 3, 'powers': [19, 1], 'representative': 174356582400, 'size': 2}
  • id: 166693046
    {'aut_label': '3B', 'centralizer': '8.b1', 'counter': 20, 'group_counter': 209, 'group_order': 6912, 'label': '3B', 'order': 3, 'powers': [20, 1], 'representative': 24536, 'size': 8}
  • id: 166693047
    {'aut_label': '3C', 'centralizer': '8.j1', 'counter': 21, 'group_counter': 209, 'group_order': 6912, 'label': '3C', 'order': 3, 'powers': [21, 1], 'representative': 7257600, 'size': 8}
  • id: 166693048
    {'aut_label': '3D', 'centralizer': '16.b1', 'counter': 22, 'group_counter': 209, 'group_order': 6912, 'label': '3D', 'order': 3, 'powers': [22, 1], 'representative': 174356606936, 'size': 16}
  • id: 166693049
    {'aut_label': '3E', 'centralizer': '16.k1', 'counter': 23, 'group_counter': 209, 'group_order': 6912, 'label': '3E', 'order': 3, 'powers': [23, 1], 'representative': 174436416000, 'size': 16}
  • id: 166693050
    {'aut_label': '3F', 'centralizer': '64.a1', 'counter': 24, 'group_counter': 209, 'group_order': 6912, 'label': '3F', 'order': 3, 'powers': [24, 1], 'representative': 7282136, 'size': 64}
  • id: 166693051
    {'aut_label': '3G', 'centralizer': '128.a1', 'counter': 25, 'group_counter': 209, 'group_order': 6912, 'label': '3G', 'order': 3, 'powers': [25, 1], 'representative': 93528715736, 'size': 128}
  • id: 166693052
    {'aut_label': '4A', 'centralizer': '6.q1', 'counter': 26, 'group_counter': 209, 'group_order': 6912, 'label': '4A', 'order': 4, 'powers': [2, 26], 'representative': 29284, 'size': 6}
  • id: 166693053
    {'aut_label': '4B', 'centralizer': '6.f1', 'counter': 27, 'group_counter': 209, 'group_order': 6912, 'label': '4B', 'order': 4, 'powers': [6, 27], 'representative': 119750400, 'size': 6}
  • id: 166693054
    {'aut_label': '4B', 'centralizer': '6.f1', 'counter': 28, 'group_counter': 209, 'group_order': 6912, 'label': '4C', 'order': 4, 'powers': [6, 28], 'representative': 119787333, 'size': 6}
  • id: 166693055
    {'aut_label': '4D', 'centralizer': '18.bk1', 'counter': 29, 'group_counter': 209, 'group_order': 6912, 'label': '4D', 'order': 4, 'powers': [2, 29], 'representative': 87109068, 'size': 18}
  • id: 166693057
    {'aut_label': '4E', 'centralizer': '18.ba1', 'counter': 30, 'group_counter': 209, 'group_order': 6912, 'label': '4E', 'order': 4, 'powers': [2, 30], 'representative': 87178301945, 'size': 18}
  • id: 166693058
    {'aut_label': '4F', 'centralizer': '18.c1', 'counter': 31, 'group_counter': 209, 'group_order': 6912, 'label': '4F', 'order': 4, 'powers': [6, 31], 'representative': 6346808133, 'size': 18}
  • id: 166693059
    {'aut_label': '4F', 'centralizer': '18.c1', 'counter': 32, 'group_counter': 209, 'group_order': 6912, 'label': '4G', 'order': 4, 'powers': [6, 32], 'representative': 6346771200, 'size': 18}
  • id: 166693060
    {'aut_label': '4H', 'centralizer': '36.m1', 'counter': 33, 'group_counter': 209, 'group_order': 6912, 'label': '4H', 'order': 4, 'powers': [2, 33], 'representative': 373625, 'size': 36}
  • id: 166693061
    {'aut_label': '4I', 'centralizer': '36.bf1', 'counter': 34, 'group_counter': 209, 'group_order': 6912, 'label': '4I', 'order': 4, 'powers': [3, 34], 'representative': 119761145, 'size': 36}
  • id: 166693062
    {'aut_label': '4J', 'centralizer': '54.r1', 'counter': 35, 'group_counter': 209, 'group_order': 6912, 'label': '4J', 'order': 4, 'powers': [2, 35], 'representative': 6267309945, 'size': 54}
  • id: 166693063
    {'aut_label': '4K', 'centralizer': '72.n1', 'counter': 36, 'group_counter': 209, 'group_order': 6912, 'label': '4K', 'order': 4, 'powers': [6, 36], 'representative': 80228326, 'size': 72}
  • id: 166693064
    {'aut_label': '4L', 'centralizer': '108.d1', 'counter': 37, 'group_counter': 209, 'group_order': 6912, 'label': '4L', 'order': 4, 'powers': [2, 37], 'representative': 6266970529, 'size': 108}
  • id: 166693065
    {'aut_label': '4M', 'centralizer': '108.w1', 'counter': 38, 'group_counter': 209, 'group_order': 6912, 'label': '4M', 'order': 4, 'powers': [3, 38], 'representative': 6314485625, 'size': 108}
  • id: 166693066
    {'aut_label': '4N', 'centralizer': '216.g1', 'counter': 39, 'group_counter': 209, 'group_order': 6912, 'label': '4N', 'order': 4, 'powers': [6, 39], 'representative': 180710611946, 'size': 216}
  • id: 166693068
    {'aut_label': '6A', 'centralizer': '2.d1', 'counter': 40, 'group_counter': 209, 'group_order': 6912, 'label': '6A', 'order': 6, 'powers': [19, 2], 'representative': 174356619333, 'size': 2}
  • id: 166693069
    {'aut_label': '6B', 'centralizer': '6.x1', 'counter': 41, 'group_counter': 209, 'group_order': 6912, 'label': '6B', 'order': 6, 'powers': [19, 6], 'representative': 174443673600, 'size': 6}
  • id: 166693070
    {'aut_label': '6C', 'centralizer': '6.x1', 'counter': 42, 'group_counter': 209, 'group_order': 6912, 'label': '6C', 'order': 6, 'powers': [19, 3], 'representative': 174443710533, 'size': 6}
  • id: 166693071
    {'aut_label': '6D', 'centralizer': '8.b1', 'counter': 43, 'group_counter': 209, 'group_order': 6912, 'label': '6D', 'order': 6, 'powers': [20, 2], 'representative': 7774, 'size': 8}
  • id: 166693072
    {'aut_label': '6E', 'centralizer': '8.j1', 'counter': 44, 'group_counter': 209, 'group_order': 6912, 'label': '6E', 'order': 6, 'powers': [21, 2], 'representative': 4028613, 'size': 8}
  • id: 166693073
    {'aut_label': '6F', 'centralizer': '12.q1', 'counter': 45, 'group_counter': 209, 'group_order': 6912, 'label': '6F', 'order': 6, 'powers': [19, 7], 'representative': 93405674880, 'size': 12}
  • id: 166693074
    {'aut_label': '6F', 'centralizer': '12.q1', 'counter': 46, 'group_counter': 209, 'group_order': 6912, 'label': '6G', 'order': 6, 'powers': [19, 8], 'representative': 93405711813, 'size': 12}
  • id: 166693075
    {'aut_label': '6H', 'centralizer': '16.b1', 'counter': 47, 'group_counter': 209, 'group_order': 6912, 'label': '6H', 'order': 6, 'powers': [22, 2], 'representative': 93405319774, 'size': 16}
  • id: 166693076
    {'aut_label': '6I', 'centralizer': '16.k1', 'counter': 48, 'group_counter': 209, 'group_order': 6912, 'label': '6I', 'order': 6, 'powers': [23, 2], 'representative': 93448894533, 'size': 16}
  • id: 166693077
    {'aut_label': '6J', 'centralizer': '24.be1', 'counter': 49, 'group_counter': 209, 'group_order': 6912, 'label': '6J', 'order': 6, 'powers': [20, 3], 'representative': 40287454, 'size': 24}
  • id: 166693079
    {'aut_label': '6K', 'centralizer': '24.bb1', 'counter': 50, 'group_counter': 209, 'group_order': 6912, 'label': '6K', 'order': 6, 'powers': [20, 4], 'representative': 6227023476, 'size': 24}
  • id: 166693080
    {'aut_label': '6K', 'centralizer': '24.bb1', 'counter': 51, 'group_counter': 209, 'group_order': 6912, 'label': '6L', 'order': 6, 'powers': [20, 5], 'representative': 6227028574, 'size': 24}
  • id: 166693081
    {'aut_label': '6M', 'centralizer': '24.db1', 'counter': 52, 'group_counter': 209, 'group_order': 6912, 'label': '6M', 'order': 6, 'powers': [21, 4], 'representative': 6231012480, 'size': 24}
  • id: 166693082
    {'aut_label': '6M', 'centralizer': '24.db1', 'counter': 53, 'group_counter': 209, 'group_order': 6912, 'label': '6N', 'order': 6, 'powers': [21, 5], 'representative': 6231049413, 'size': 24}
  • id: 166693083
    {'aut_label': '6O', 'centralizer': '24.bo1', 'counter': 54, 'group_counter': 209, 'group_order': 6912, 'label': '6O', 'order': 6, 'powers': [19, 11], 'representative': 93405312746, 'size': 24}
  • id: 166693084
    {'aut_label': '6P', 'centralizer': '24.be1', 'counter': 55, 'group_counter': 209, 'group_order': 6912, 'label': '6P', 'order': 6, 'powers': [20, 6], 'representative': 87094394, 'size': 24}
  • id: 166693085
    {'aut_label': '6Q', 'centralizer': '48.h1', 'counter': 56, 'group_counter': 209, 'group_order': 6912, 'label': '6Q', 'order': 6, 'powers': [20, 7], 'representative': 365556, 'size': 48}
  • id: 166693086
    {'aut_label': '6Q', 'centralizer': '48.h1', 'counter': 57, 'group_counter': 209, 'group_order': 6912, 'label': '6R', 'order': 6, 'powers': [20, 8], 'representative': 370654, 'size': 48}
  • id: 166693087
    {'aut_label': '6S', 'centralizer': '48.bn1', 'counter': 58, 'group_counter': 209, 'group_order': 6912, 'label': '6S', 'order': 6, 'powers': [22, 3], 'representative': 93445599454, 'size': 48}
  • id: 166693088
    {'aut_label': '6T', 'centralizer': '48.bn1', 'counter': 59, 'group_counter': 209, 'group_order': 6912, 'label': '6T', 'order': 6, 'powers': [22, 6], 'representative': 174443680451, 'size': 48}
  • id: 166693090
    {'aut_label': '6U', 'centralizer': '64.a1', 'counter': 60, 'group_counter': 209, 'group_order': 6912, 'label': '6U', 'order': 6, 'powers': [24, 2], 'representative': 3999454, 'size': 64}
  • id: 166693091
    {'aut_label': '6V', 'centralizer': '72.ir1', 'counter': 61, 'group_counter': 209, 'group_order': 6912, 'label': '6V', 'order': 6, 'powers': [20, 9], 'representative': 6267303156, 'size': 72}
  • id: 166693092
    {'aut_label': '6V', 'centralizer': '72.ir1', 'counter': 62, 'group_counter': 209, 'group_order': 6912, 'label': '6W', 'order': 6, 'powers': [20, 10], 'representative': 6267308254, 'size': 72}
  • id: 166693093
    {'aut_label': '6X', 'centralizer': '72.jf1', 'counter': 63, 'group_counter': 209, 'group_order': 6912, 'label': '6X', 'order': 6, 'powers': [19, 14], 'representative': 93445592426, 'size': 72}
  • id: 166693094
    {'aut_label': '6Y', 'centralizer': '96.g1', 'counter': 64, 'group_counter': 209, 'group_order': 6912, 'label': '6Y', 'order': 6, 'powers': [22, 7], 'representative': 174360214394, 'size': 96}
  • id: 166693095
    {'aut_label': '6Z', 'centralizer': '96.be1', 'counter': 65, 'group_counter': 209, 'group_order': 6912, 'label': '6Z', 'order': 6, 'powers': [21, 11], 'representative': 7258346, 'size': 96}
  • id: 166693096
    {'aut_label': '6Y', 'centralizer': '96.g1', 'counter': 66, 'group_counter': 209, 'group_order': 6912, 'label': '6AA', 'order': 6, 'powers': [22, 8], 'representative': 174364219633, 'size': 96}
  • id: 166693097
    {'aut_label': '6AB', 'centralizer': '128.a1', 'counter': 67, 'group_counter': 209, 'group_order': 6912, 'label': '6AB', 'order': 6, 'powers': [25, 2], 'representative': 174440415454, 'size': 128}
  • id: 166693098
    {'aut_label': '6AC', 'centralizer': '144.w1', 'counter': 68, 'group_counter': 209, 'group_order': 6912, 'label': '6AC', 'order': 6, 'powers': [19, 16], 'representative': 174364203626, 'size': 144}
  • id: 166693099
    {'aut_label': '6AD', 'centralizer': '144.e1', 'counter': 69, 'group_counter': 209, 'group_order': 6912, 'label': '6AD', 'order': 6, 'powers': [20, 12], 'representative': 6227409790, 'size': 144}
  • id: 166693101
    {'aut_label': '6AD', 'centralizer': '144.e1', 'counter': 70, 'group_counter': 209, 'group_order': 6912, 'label': '6AE', 'order': 6, 'powers': [20, 13], 'representative': 180591236995, 'size': 144}
  • id: 166693102
    {'aut_label': '6AF', 'centralizer': '192.c1', 'counter': 71, 'group_counter': 209, 'group_order': 6912, 'label': '6AF', 'order': 6, 'powers': [24, 5], 'representative': 87221844574, 'size': 192}
  • id: 166693103
    {'aut_label': '6AF', 'centralizer': '192.c1', 'counter': 72, 'group_counter': 209, 'group_order': 6912, 'label': '6AG', 'order': 6, 'powers': [24, 4], 'representative': 87221839476, 'size': 192}
  • id: 166693104
    {'aut_label': '6AH', 'centralizer': '192.l1', 'counter': 73, 'group_counter': 209, 'group_order': 6912, 'label': '6AH', 'order': 6, 'powers': [23, 11], 'representative': 93412571412, 'size': 192}
  • id: 166693105
    {'aut_label': '6AI', 'centralizer': '288.cd1', 'counter': 74, 'group_counter': 209, 'group_order': 6912, 'label': '6AI', 'order': 6, 'powers': [21, 15], 'representative': 6234292887, 'size': 288}
  • id: 166693106
    {'aut_label': '8A1', 'centralizer': '6.q1', 'counter': 75, 'group_counter': 209, 'group_order': 6912, 'label': '8A1', 'order': 8, 'powers': [26, 75], 'representative': 34578, 'size': 6}
  • id: 166693107
    {'aut_label': '8A1', 'centralizer': '6.q1', 'counter': 76, 'group_counter': 209, 'group_order': 6912, 'label': '8A-1', 'order': 8, 'powers': [26, 76], 'representative': 11974, 'size': 6}
  • id: 166693108
    {'aut_label': '8B1', 'centralizer': '18.bk1', 'counter': 77, 'group_counter': 209, 'group_order': 6912, 'label': '8B1', 'order': 8, 'powers': [26, 77], 'representative': 40314258, 'size': 18}
  • id: 166693109
    {'aut_label': '8B1', 'centralizer': '18.bk1', 'counter': 78, 'group_counter': 209, 'group_order': 6912, 'label': '8B-1', 'order': 8, 'powers': [26, 78], 'representative': 40291654, 'size': 18}
  • id: 166693110
    {'aut_label': '8C1', 'centralizer': '18.ba1', 'counter': 79, 'group_counter': 209, 'group_order': 6912, 'label': '8C1', 'order': 8, 'powers': [26, 79], 'representative': 180583637410, 'size': 18}
  • id: 166693112
    {'aut_label': '8C1', 'centralizer': '18.ba1', 'counter': 80, 'group_counter': 209, 'group_order': 6912, 'label': '8C-1', 'order': 8, 'powers': [26, 80], 'representative': 180583622348, 'size': 18}
  • id: 166693113
    {'aut_label': '8D1', 'centralizer': '36.m1', 'counter': 81, 'group_counter': 209, 'group_order': 6912, 'label': '8D1', 'order': 8, 'powers': [26, 81], 'representative': 397458, 'size': 36}
  • id: 166693114
    {'aut_label': '8D1', 'centralizer': '36.m1', 'counter': 82, 'group_counter': 209, 'group_order': 6912, 'label': '8D-1', 'order': 8, 'powers': [26, 82], 'representative': 374854, 'size': 36}
  • id: 166693115
    {'aut_label': '8E1', 'centralizer': '36.bf1', 'counter': 83, 'group_counter': 209, 'group_order': 6912, 'label': '8E1', 'order': 8, 'powers': [29, 83], 'representative': 119784978, 'size': 36}
  • id: 166693116
    {'aut_label': '8E1', 'centralizer': '36.bf1', 'counter': 84, 'group_counter': 209, 'group_order': 6912, 'label': '8E-1', 'order': 8, 'powers': [29, 84], 'representative': 43920454, 'size': 36}
  • id: 166693117
    {'aut_label': '8F1', 'centralizer': '54.r1', 'counter': 85, 'group_counter': 209, 'group_order': 6912, 'label': '8F1', 'order': 8, 'powers': [26, 85], 'representative': 6267308691, 'size': 54}
  • id: 166693118
    {'aut_label': '8F1', 'centralizer': '54.r1', 'counter': 86, 'group_counter': 209, 'group_order': 6912, 'label': '8F-1', 'order': 8, 'powers': [26, 86], 'representative': 6267309595, 'size': 54}
  • id: 166693119
    {'aut_label': '8G1', 'centralizer': '108.d1', 'counter': 87, 'group_counter': 209, 'group_order': 6912, 'label': '8G1', 'order': 8, 'powers': [26, 87], 'representative': 6266966185, 'size': 108}
  • id: 166693120
    {'aut_label': '8G1', 'centralizer': '108.d1', 'counter': 88, 'group_counter': 209, 'group_order': 6912, 'label': '8G-1', 'order': 8, 'powers': [26, 88], 'representative': 6266960382, 'size': 108}
  • id: 166693121
    {'aut_label': '8H1', 'centralizer': '108.w1', 'counter': 89, 'group_counter': 209, 'group_order': 6912, 'label': '8H1', 'order': 8, 'powers': [29, 89], 'representative': 6307229254, 'size': 108}
  • id: 166693123
    {'aut_label': '8H1', 'centralizer': '108.w1', 'counter': 90, 'group_counter': 209, 'group_order': 6912, 'label': '8H-1', 'order': 8, 'powers': [29, 90], 'representative': 6274229778, 'size': 108}
  • id: 166693124
    {'aut_label': '12A', 'centralizer': '12.ba1', 'counter': 91, 'group_counter': 209, 'group_order': 6912, 'label': '12A', 'order': 12, 'powers': [41, 27], 'representative': 93449220480, 'size': 12}
  • id: 166693125
    {'aut_label': '12A', 'centralizer': '12.ba1', 'counter': 92, 'group_counter': 209, 'group_order': 6912, 'label': '12B', 'order': 12, 'powers': [41, 28], 'representative': 93449257413, 'size': 12}
  • id: 166693126
    {'aut_label': '12C', 'centralizer': '12.cc1', 'counter': 93, 'group_counter': 209, 'group_order': 6912, 'label': '12C', 'order': 12, 'powers': [40, 26], 'representative': 174356611684, 'size': 12}
  • id: 166693127
    {'aut_label': '12D', 'centralizer': '36.hb1', 'counter': 94, 'group_counter': 209, 'group_order': 6912, 'label': '12D', 'order': 12, 'powers': [40, 29], 'representative': 174443702884, 'size': 36}
  • id: 166693128
    {'aut_label': '12E', 'centralizer': '48.l1', 'counter': 95, 'group_counter': 209, 'group_order': 6912, 'label': '12E', 'order': 12, 'powers': [55, 27], 'representative': 43911156, 'size': 48}
  • id: 166693129
    {'aut_label': '12E', 'centralizer': '48.l1', 'counter': 96, 'group_counter': 209, 'group_order': 6912, 'label': '12F', 'order': 12, 'powers': [55, 28], 'representative': 43916254, 'size': 48}
  • id: 166693130
    {'aut_label': '12G', 'centralizer': '48.da1', 'counter': 97, 'group_counter': 209, 'group_order': 6912, 'label': '12G', 'order': 12, 'powers': [44, 26], 'representative': 7286884, 'size': 48}
  • id: 166693131
    {'aut_label': '12H', 'centralizer': '72.cb1', 'counter': 98, 'group_counter': 209, 'group_order': 6912, 'label': '12H', 'order': 12, 'powers': [40, 33], 'representative': 93405684345, 'size': 72}
  • id: 166693132
    {'aut_label': '12I', 'centralizer': '72.hf1', 'counter': 99, 'group_counter': 209, 'group_order': 6912, 'label': '12I', 'order': 12, 'powers': [42, 34], 'representative': 93449229945, 'size': 72}
  • id: 166693015
    {'aut_label': '12J', 'centralizer': '96.da1', 'counter': 100, 'group_counter': 209, 'group_order': 6912, 'label': '12J', 'order': 12, 'powers': [48, 26], 'representative': 174436439444, 'size': 96}
  • id: 166693016
    {'aut_label': '12K', 'centralizer': '96.p1', 'counter': 101, 'group_counter': 209, 'group_order': 6912, 'label': '12K', 'order': 12, 'powers': [59, 28], 'representative': 93449250043, 'size': 96}
  • id: 166693017
    {'aut_label': '12K', 'centralizer': '96.p1', 'counter': 102, 'group_counter': 209, 'group_order': 6912, 'label': '12L', 'order': 12, 'powers': [59, 27], 'representative': 93485515331, 'size': 96}
  • id: 166693018
    {'aut_label': '12M', 'centralizer': '144.hp1', 'counter': 103, 'group_counter': 209, 'group_order': 6912, 'label': '12M', 'order': 12, 'powers': [44, 30], 'representative': 87221846265, 'size': 144}
  • id: 166693019
    {'aut_label': '12N', 'centralizer': '144.cd1', 'counter': 104, 'group_counter': 209, 'group_order': 6912, 'label': '12N', 'order': 12, 'powers': [41, 36], 'representative': 174403788646, 'size': 144}
  • id: 166693020
    {'aut_label': '12O', 'centralizer': '144.i1', 'counter': 105, 'group_counter': 209, 'group_order': 6912, 'label': '12O', 'order': 12, 'powers': [55, 31], 'representative': 6270969399, 'size': 144}
  • id: 166693021
    {'aut_label': '12O', 'centralizer': '144.i1', 'counter': 106, 'group_counter': 209, 'group_order': 6912, 'label': '12P', 'order': 12, 'powers': [55, 32], 'representative': 6270945007, 'size': 144}
  • id: 166693022
    {'aut_label': '24A1', 'centralizer': '12.cc1', 'counter': 107, 'group_counter': 209, 'group_order': 6912, 'label': '24A1', 'order': 24, 'powers': [93, 75], 'representative': 93405320211, 'size': 12}
  • id: 166693023
    {'aut_label': '24A1', 'centralizer': '12.cc1', 'counter': 108, 'group_counter': 209, 'group_order': 6912, 'label': '24A-1', 'order': 24, 'powers': [93, 76], 'representative': 93405321115, 'size': 12}
  • id: 166693024
    {'aut_label': '24B1', 'centralizer': '36.hb1', 'counter': 109, 'group_counter': 209, 'group_order': 6912, 'label': '24B1', 'order': 24, 'powers': [93, 77], 'representative': 93445599891, 'size': 36}
  • id: 166693026
    {'aut_label': '24B1', 'centralizer': '36.hb1', 'counter': 110, 'group_counter': 209, 'group_order': 6912, 'label': '24B-1', 'order': 24, 'powers': [93, 78], 'representative': 93445600795, 'size': 36}
  • id: 166693027
    {'aut_label': '24C1', 'centralizer': '48.da1', 'counter': 111, 'group_counter': 209, 'group_order': 6912, 'label': '24C1', 'order': 24, 'powers': [97, 75], 'representative': 3999891, 'size': 48}
  • id: 166693028
    {'aut_label': '24C1', 'centralizer': '48.da1', 'counter': 112, 'group_counter': 209, 'group_order': 6912, 'label': '24C-1', 'order': 24, 'powers': [97, 76], 'representative': 4000795, 'size': 48}
  • id: 166693029
    {'aut_label': '24D1', 'centralizer': '72.cb1', 'counter': 113, 'group_counter': 209, 'group_order': 6912, 'label': '24D1', 'order': 24, 'powers': [93, 81], 'representative': 93405683091, 'size': 72}
  • id: 166693030
    {'aut_label': '24D1', 'centralizer': '72.cb1', 'counter': 114, 'group_counter': 209, 'group_order': 6912, 'label': '24D-1', 'order': 24, 'powers': [93, 82], 'representative': 93405683995, 'size': 72}
  • id: 166693031
    {'aut_label': '24E1', 'centralizer': '72.hf1', 'counter': 115, 'group_counter': 209, 'group_order': 6912, 'label': '24E1', 'order': 24, 'powers': [94, 83], 'representative': 93449228691, 'size': 72}
  • id: 166693032
    {'aut_label': '24E1', 'centralizer': '72.hf1', 'counter': 116, 'group_counter': 209, 'group_order': 6912, 'label': '24E-1', 'order': 24, 'powers': [94, 84], 'representative': 93449229595, 'size': 72}
  • id: 166693033
    {'aut_label': '24F1', 'centralizer': '96.da1', 'counter': 117, 'group_counter': 209, 'group_order': 6912, 'label': '24F1', 'order': 24, 'powers': [100, 75], 'representative': 93448883506, 'size': 96}
  • id: 166693034
    {'aut_label': '24F1', 'centralizer': '96.da1', 'counter': 118, 'group_counter': 209, 'group_order': 6912, 'label': '24F-1', 'order': 24, 'powers': [100, 76], 'representative': 174436425115, 'size': 96}
  • id: 166693035
    {'aut_label': '24G1', 'centralizer': '144.hp1', 'counter': 119, 'group_counter': 209, 'group_order': 6912, 'label': '24G1', 'order': 24, 'powers': [97, 79], 'representative': 180703745065, 'size': 144}
  • id: 166693037
    {'aut_label': '24G1', 'centralizer': '144.hp1', 'counter': 120, 'group_counter': 209, 'group_order': 6912, 'label': '24G-1', 'order': 24, 'powers': [97, 80], 'representative': 180631163262, 'size': 144}
• gps_qchar •

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

  
  
  • id: 16663307
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663324
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663335
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663346
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663357
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663368
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663379
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663390
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663401
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, -1, 2, 2, -1, -1, 2, -1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0, -1, 2, -1, -1, 2, 2, 2, -1, 0, 0, 2, -1, -1, -1, 0, 0, -1, 0, 0, -1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663308
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, -1, 2, -1, -1, -1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 0, 0, 2, -1, 2, 2, 2, -1, -1, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, -1, 0, 0, -1, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663315
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, -1, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 0, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663316
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 2, 2, 0, 2, 2, 2, -1, 2, -2, -2, -1, 2, -1, 1, 1, -2, -2, 0, -1, -1, -1, 1, 1, -1, 0, 1, 1, 0, 1, 1, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 1, 1, 2, -2, -2, 2, 1, 1, -2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663317
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, 0, -2, -2, -2, 0, 0, -2, 2, 0, 2, 0, 2, 2, -1, 2, -1, -1, -1, 2, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 0, 0, 2, -1, 2, -2, -2, 1, 1, -2, 2, 2, 2, 0, 0, -1, -2, -2, -2, 1, 0, 0, -1, 0, 0, 0, 1, 1, 1, -1, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663318
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, 0, -2, -2, 2, 0, 0, 2, -2, 0, -2, 0, 2, 2, -1, 2, -1, -1, -1, 2, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 0, 0, 2, -1, 2, -2, -2, 1, 1, 2, 2, 2, 2, 0, 0, -1, 2, -2, -2, -1, 0, 0, -1, 0, 0, 0, 1, 1, -1, 1, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663319
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, 2, 2, -2, -2, 2, -2, 2, 2, -2, 0, -2, -2, 0, 2, 2, 2, -1, 2, 2, 2, -1, 2, -1, 1, 1, -2, -2, 0, -1, -1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, -1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663320
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, -1, 2, 2, -1, -1, 2, -1, 2, -2, -2, 0, 0, 2, 0, -2, -2, 0, 2, 0, 0, 0, -1, -1, -1, 2, 2, 1, 1, -1, -1, 2, 0, 0, 0, 0, 1, 2, -1, -1, -2, -2, 2, 1, 0, 0, -2, 1, 1, -1, 0, 0, -1, 0, 0, 1, 0, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -2, -2, 2, 1, 1, -1, 1, 1, 0, 0, -1, 0, 1, 1, 1, 1, -2, -2, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663321
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, -1, 2, 2, -1, -1, 2, -1, 2, -2, -2, 0, 0, 2, 0, -2, -2, 0, -2, 0, 0, 0, -1, -1, -1, 2, 2, 1, 1, -1, -1, 2, 0, 0, 0, 0, -1, 2, -1, -1, -2, -2, 2, -1, 0, 0, 2, 1, 1, -1, 0, 0, 1, 0, 0, -1, 0, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -2, -2, 2, 1, 1, -1, 1, 1, 0, 0, 1, 0, -1, -1, -1, -1, 2, 2, 1, 1, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663322
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -1, 2, 2, -1, -1, 2, -1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, -2, 0, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0, 1, 2, -1, -1, 2, 2, 2, 1, 0, 0, -2, -1, -1, -1, 0, 0, 1, 0, 0, 1, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 1, 0, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663323
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 0, -2, -2, 0, 2, 2, 2, -1, 2, -2, -2, -1, 2, -1, -1, -1, 2, 2, 0, -1, -1, -1, 1, 1, -1, 0, -1, -1, 0, 1, 1, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 1, 1, 2, -2, -2, 2, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663325
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, 2, -2, 0, 0, -2, -2, 0, -2, 0, 2, 2, -1, 2, -1, -1, -1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 0, 0, 2, -1, 2, 2, 2, -1, -1, -2, 2, 2, 2, 0, 0, -1, -2, 2, 2, 1, 0, 0, -1, 0, 0, 0, -1, -1, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663330
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 1, 1, -1, -1, 3, 1, 1, -1, 3, 1, -1, 1, 3, 3, 0, 3, 0, 0, 0, 3, -1, -1, 3, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 3, -1, -1, 3, 0, 1, 1, 3, 0, -1, 3, 3, 0, 0, 3, -1, -1, -1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 3, 3, -1, -1, 3, 3, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 3, -1, -1, -1, -1, -1, 0, 1, -1, 0, -1, -1, 0, -1, -1, -1, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663331
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 1, 1, 1, 1, 1, 3, 0, 3, 0, 3, 0, 0, -1, 3, 3, -1, 3, -1, 3, -1, -1, -1, 1, -1, -1, 1, 3, 3, 3, 0, 3, 3, 3, 0, 3, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 0, 0, -1, -1, -1, -1, 0, 0, -1, 0, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663332
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3c', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, 3, 0, 3, 0, 0, 0, 3, 1, 1, 3, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 3, -1, -1, 3, 0, -1, -1, 3, 0, -1, 3, 3, 0, 0, 3, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, 0, -1, -1, -1, 0, 0, 0, 0, 3, 3, -1, -1, 3, 3, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 3, 1, 1, -1, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, 1, 1, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663333
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 3, 0, 3, 0, 3, 0, 0, -1, 3, 3, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 0, 3, 3, 3, 0, 3, 0, 0, 0, 3, 3, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 3, 3, -1, 0, 0, -1, -1, -1, -1, 0, 0, -1, 0, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663334
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, -1, -1, -1, 1, 1, -3, 1, 1, 1, 3, 1, -1, -1, 3, 3, 0, 3, 0, 0, 0, 3, 1, 1, -3, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 3, -1, -1, 3, 0, -1, -1, 3, 0, -1, -3, -3, 0, 0, -3, -1, -1, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, -3, -3, 1, 1, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 3, 1, 1, -1, 1, 1, 0, -1, 1, 0, 1, 1, 0, -1, -1, -1, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663336
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, -1, -1, -1, 1, 1, 3, 1, 1, -1, -3, -1, 1, 1, 3, 3, 0, 3, 0, 0, 0, 3, 1, 1, -3, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 3, -1, -1, 3, 0, -1, -1, 3, 0, -1, -3, -3, 0, 0, 3, -1, -1, -1, -1, -1, 0, -1, 1, 1, 0, -1, -1, 0, 1, 1, -1, 0, 0, 0, 0, 3, 3, -1, -1, -3, -3, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 3, 1, 1, -1, 1, 1, 0, -1, 1, 0, 1, 1, 0, -1, 1, -1, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663337
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, -1, 1, 1, 1, 1, -3, -1, -1, 1, 3, -1, -1, 1, 3, 3, 0, 3, 0, 0, 0, 3, -1, -1, -3, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 3, -1, -1, 3, 0, 1, 1, 3, 0, -1, -3, -3, 0, 0, -3, -1, -1, -1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, -1, -1, -1, 0, 0, 0, 0, -3, -3, 1, 1, 3, 3, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 3, -1, -1, -1, -1, -1, 0, 1, -1, 0, -1, -1, 0, 1, 1, 1, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663338
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -1, -1, 1, 1, 1, 1, 3, -1, -1, -1, -3, 1, 1, -1, 3, 3, 0, 3, 0, 0, 0, 3, -1, -1, -3, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 3, -1, -1, 3, 0, 1, 1, 3, 0, -1, -3, -3, 0, 0, 3, -1, -1, -1, 1, 1, 0, -1, 1, 1, 0, 1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 3, 3, -1, -1, -3, -3, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 3, -1, -1, -1, -1, -1, 0, 1, -1, 0, -1, -1, 0, 1, -1, 1, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663339
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, 3, -3, -3, -3, -3, -1, 3, 3, -1, 1, 1, 1, -1, 3, 0, 3, 0, 3, 0, 0, -1, -3, -3, 1, 3, -1, 3, 1, 1, 1, 1, -1, -1, -1, 3, 3, 3, 0, 3, -3, -3, 0, 3, 0, 0, 0, -3, -3, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -3, -3, -1, 0, 0, -1, 1, 1, -1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663340
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, 3, -3, -3, -3, -3, 1, 3, 3, 1, -1, -1, -1, 1, 3, 0, 3, 0, 3, 0, 0, -1, -3, -3, 1, 3, -1, 3, 1, 1, 1, -1, -1, -1, 1, 3, 3, 3, 0, 3, -3, -3, 0, 3, 0, 0, 0, -3, -3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -3, -3, -1, 0, 0, -1, 1, 1, -1, 0, 0, 1, 0, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663341
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, 3, 3, 3, -3, -3, -1, -3, -3, -1, 1, -1, 1, 1, 3, 0, 3, 0, 3, 0, 0, -1, 3, 3, 1, -3, -1, -3, -1, -1, 1, -1, 1, 1, 1, 3, 3, 3, 0, 3, 3, 3, 0, 3, 0, 0, 0, -3, -3, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 0, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663342
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, 3, 3, 3, -3, -3, 1, -3, -3, 1, -1, 1, -1, -1, 3, 0, 3, 0, 3, 0, 0, -1, 3, 3, 1, -3, -1, -3, -1, -1, 1, 1, 1, 1, -1, 3, 3, 3, 0, 3, 3, 3, 0, 3, 0, 0, 0, -3, -3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 3, 3, -1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 0, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663343
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3m', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -3, -1, -1, 1, -3, 1, 1, 1, 3, 3, 0, 3, 0, 0, 0, 3, 1, 1, 3, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 3, -1, -1, 3, 0, -1, -1, 3, 0, -1, 3, 3, 0, 0, -3, -1, -1, -1, -1, -1, 0, 1, -1, -1, 0, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -3, -3, 1, 1, -3, -3, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 3, 1, 1, -1, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 1, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663344
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3n', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 1, 1, -1, -1, -3, 1, 1, 1, -3, -1, 1, -1, 3, 3, 0, 3, 0, 0, 0, 3, -1, -1, 3, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 3, -1, -1, 3, 0, 1, 1, 3, 0, -1, 3, 3, 0, 0, -3, -1, -1, -1, 1, 1, 0, 1, -1, -1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 0, 0, -3, -3, 1, 1, -3, -3, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 3, -1, -1, -1, -1, -1, 0, 1, -1, 0, -1, -1, 0, -1, 1, -1, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663345
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3o', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 3, 3, -1, -3, -3, -1, -1, 1, -1, 1, 3, 0, 3, 0, 3, 0, 0, -1, -3, -3, -1, -3, -1, -3, 1, 1, -1, 1, 1, 1, 1, 3, 3, 3, 0, 3, -3, -3, 0, 3, 0, 0, 0, 3, 3, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -3, -3, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 0, 1, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663347
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.3p', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 3, 3, 1, -3, -3, 1, 1, -1, 1, -1, 3, 0, 3, 0, 3, 0, 0, -1, -3, -3, -1, -3, -1, -3, 1, 1, -1, -1, 1, 1, -1, 3, 3, 3, 0, 3, -3, -3, 0, 3, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -3, -3, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 0, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663326
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2m', 'multiplicity': 2, 'nt': [24, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, 4, -2, 4, -2, 4, -2, -2, 0, -4, 4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 2, -4, -4, 4, 2, -4, 2, 2, -2, -4, 4, 0, -2, 2, -2, 2, -2, 2, 0, 2, -2, 0, -2, 2, 2, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663327
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2n', 'multiplicity': 2, 'nt': [24, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, -4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, 4, -2, 4, -2, 4, -2, -2, 0, 4, -4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 2, -4, 4, -4, 2, -4, 2, 2, -2, -4, 4, 0, -2, 2, -2, -2, 2, 2, 0, 2, -2, 0, 2, -2, 2, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663328
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2o', 'multiplicity': 2, 'nt': [24, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, -4, 4, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 4, -2, 4, -2, 4, -2, -2, 0, -4, 4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 2, -4, -4, 4, 2, -4, 2, -2, 2, 4, -4, 0, -2, 2, -2, 2, -2, 2, 0, -2, 2, 0, -2, 2, 2, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663329
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.2p', 'multiplicity': 2, 'nt': [24, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 4, -2, 4, -2, 4, -2, -2, 0, 4, -4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 2, -4, 4, -4, 2, -4, 2, -2, 2, 4, -4, 0, -2, 2, -2, -2, 2, 2, 0, -2, 2, 0, 2, -2, 2, -2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663348
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 0, 0, -2, 1, 4, 0, 0, 0, 0, -2, 4, -2, -2, 0, 0, -2, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663349
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, 4, 4, 4, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, -2, 1, 1, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663350
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 4, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 0, -2, -2, -2, 0, 0, 1, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663351
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4d', 'multiplicity': 1, 'nt': [8, 23], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, 4, 1, 4, 1, 4, 1, 1, 0, -4, 4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -1, -4, -4, 4, -1, -4, -1, -1, 1, -4, 4, 0, 1, -1, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, -1, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663352
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4e', 'multiplicity': 1, 'nt': [8, 23], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, -4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, 4, 1, 4, 1, 4, 1, 1, 0, 4, -4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -1, -4, 4, -4, -1, -4, -1, -1, 1, -4, 4, 0, 1, -1, 1, 1, -1, -1, 0, -1, 1, 0, -1, 1, -1, -1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663353
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4f', 'multiplicity': 1, 'nt': [8, 23], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, -4, 4, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 4, 1, 4, 1, 4, 1, 1, 0, -4, 4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -1, -4, -4, 4, -1, -4, -1, 1, -1, 4, -4, 0, 1, -1, 1, -1, 1, -1, 0, 1, -1, 0, 1, -1, -1, -1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663354
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4g', 'multiplicity': 1, 'nt': [8, 23], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 4, 1, 4, 1, 4, 1, 1, 0, 4, -4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -1, -4, 4, -4, -1, -4, -1, 1, -1, 4, -4, 0, 1, -1, 1, 1, -1, -1, 0, 1, -1, 0, -1, 1, -1, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663355
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4h', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4, 0, 0, -4, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 4, 4, -2, -2, 0, 0, -2, -2, -2, 2, 2, 2, 2, 0, -2, -2, -2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663356
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4i', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, 4, -4, -4, 0, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, 2, 2, 1, -2, -2, 0, 0, 0, 0, 0, -2, 1, 1, 2, 2, -2, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 2, 4, 2, 2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663358
    {'cdim': 4, 'counter': 50, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4j', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 0, 0, -2, 1, 4, 0, 0, 0, 0, 2, 4, -2, -2, 0, 0, -2, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663363
    {'cdim': 6, 'counter': 55, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6a', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -2, -2, 2, 2, 0, 0, 6, 0, 0, -2, 0, 2, 0, 0, -3, 6, 0, -3, 0, 0, 0, 6, -2, -2, 0, 0, -2, 0, 2, -2, 0, -2, 0, 0, 0, -3, 1, 1, 6, 0, -1, -1, -3, 0, -2, 0, 0, 0, 0, -3, -2, 1, 1, 2, 2, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 6, 6, -2, -2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, -2, -2, 0, -1, 1, 0, 1, 1, 0, 0, 1, 0, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663364
    {'cdim': 6, 'counter': 56, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6b', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, 6, 6, 6, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, -3, 0, 6, 0, -3, 0, 0, -2, 6, 6, 0, 0, -2, 0, -2, -2, 0, 2, 0, 0, 0, -3, -3, -3, 0, 6, -3, -3, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, -3, -3, 1, 0, 0, -2, 1, 1, 1, 0, 0, 0, 0, -1, 0, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663365
    {'cdim': 6, 'counter': 57, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6c', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, 2, 2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 6, -2, -2, 6, -2, -2, -2, 2, -2, -2, 0, 2, -2, 0, 6, -2, -2, -3, 0, 2, 2, -3, 0, 1, -3, -3, 0, 0, 0, 1, 1, 1, -1, -1, 0, 0, 1, 1, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, -2, -2, 1, 1, 0, 2, -2, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663366
    {'cdim': 6, 'counter': 58, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6d', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 2, 0, 0, 2, 2, 0, 2, 0, 6, 0, -3, 0, -3, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 6, 6, 6, 0, -3, 0, 0, 0, -3, 0, 0, 0, -3, -3, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16663367
    {'cdim': 6, 'counter': 59, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6e', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -2, -2, -2, -2, 0, 0, 6, 0, 0, -2, 0, -2, 0, 0, -3, 6, 0, -3, 0, 0, 0, 6, 2, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, -3, 1, 1, 6, 0, 1, 1, -3, 0, -2, 0, 0, 0, 0, -3, -2, 1, 1, -2, -2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 6, 6, -2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -3, -1, -1, 1, 2, 2, 0, 1, -1, 0, -1, -1, 0, 0, -1, 0, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663369
    {'cdim': 6, 'counter': 60, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6f', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, 6, 6, 6, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -3, 0, 6, 0, -3, 0, 0, -2, 6, 6, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, 0, -3, -3, -3, 0, 6, -3, -3, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, -3, -3, 1, 0, 0, -2, 1, 1, 1, 0, 0, 0, 0, 1, 0, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663370
    {'cdim': 6, 'counter': 61, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6g', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 6, 2, 2, 6, 2, -2, 2, -2, 2, -2, 0, -2, 2, 0, 6, -2, -2, -3, 0, -2, -2, -3, 0, 1, -3, -3, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, -2, -1, -1, 0, -2, 2, 0, -1, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663371
    {'cdim': 6, 'counter': 62, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6h', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 0, 0, 6, 6, -2, 0, 0, -2, -2, 0, -2, 0, 6, 0, -3, 0, -3, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 6, 6, 6, 0, -3, 0, 0, 0, -3, 0, 0, 0, -3, -3, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16663372
    {'cdim': 6, 'counter': 63, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6i', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, -2, -2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 6, 2, 2, -6, -2, -2, -2, -2, 2, 2, 0, 2, -2, 0, 6, -2, -2, -3, 0, -2, -2, -3, 0, 1, 3, 3, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, -2, -1, -1, 0, -2, 2, 0, -1, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663373
    {'cdim': 6, 'counter': 64, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6j', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, -2, 2, 2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 6, -2, -2, -6, 2, -2, 2, 2, -2, 2, 0, -2, 2, 0, 6, -2, -2, -3, 0, 2, 2, -3, 0, 1, 3, 3, 0, 0, 0, 1, 1, 1, -1, -1, 0, 0, -1, -1, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -2, -2, -2, 1, 1, 0, 2, -2, 0, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663374
    {'cdim': 6, 'counter': 65, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6k', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, 6, 0, 0, -6, -6, -2, 0, 0, -2, 2, 0, 2, 0, 6, 0, -3, 0, -3, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 6, 6, 6, 0, -3, 0, 0, 0, -3, 0, 0, 0, 3, 3, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16663375
    {'cdim': 6, 'counter': 66, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6l', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, 6, 0, 0, -6, -6, 2, 0, 0, 2, -2, 0, -2, 0, 6, 0, -3, 0, -3, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 6, 6, 6, 0, -3, 0, 0, 0, -3, 0, 0, 0, 3, 3, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16663376
    {'cdim': 6, 'counter': 67, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6m', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -2, -2, -2, -2, 0, 0, -6, 0, 0, 2, 0, 2, 0, 0, -3, 6, 0, -3, 0, 0, 0, 6, 2, 2, 0, 0, -2, 0, -2, 2, 0, -2, 0, 0, 0, -3, 1, 1, 6, 0, 1, 1, -3, 0, -2, 0, 0, 0, 0, 3, -2, 1, 1, -2, -2, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, -6, -6, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -3, -1, -1, 1, 2, 2, 0, 1, -1, 0, -1, -1, 0, 0, 1, 0, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663377
    {'cdim': 6, 'counter': 68, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6n', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -2, -2, 2, 2, 0, 0, -6, 0, 0, 2, 0, -2, 0, 0, -3, 6, 0, -3, 0, 0, 0, 6, -2, -2, 0, 0, -2, 0, 2, -2, 0, 2, 0, 0, 0, -3, 1, 1, 6, 0, -1, -1, -3, 0, -2, 0, 0, 0, 0, 3, -2, 1, 1, 2, 2, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, -6, -6, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, -2, -2, 0, -1, 1, 0, 1, 1, 0, 0, -1, 0, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663378
    {'cdim': 6, 'counter': 69, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6o', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, 6, -6, -6, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, -3, 0, 6, 0, -3, 0, 0, -2, -6, -6, 0, 0, -2, 0, 2, 2, 0, 2, 0, 0, 0, -3, -3, -3, 0, 6, 3, 3, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, -2, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1, -1, -1, -1, 2, 2, 1, 1, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663380
    {'cdim': 6, 'counter': 70, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6p', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, 6, -6, -6, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, -3, 0, 6, 0, -3, 0, 0, -2, -6, -6, 0, 0, -2, 0, 2, 2, 0, -2, 0, 0, 0, -3, -3, -3, 0, 6, 3, 3, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, -2, -1, -1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, -2, -2, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663359
    {'cdim': 4, 'counter': 51, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4k', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -8, 8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 4, 4, 0, 0, 4, 4, 4, 4, -4, 4, -4, 0, -4, 4, -4, 0, 0, -2, 0, 4, -4, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663360
    {'cdim': 4, 'counter': 52, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4l', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 8, 2, -4, -4, 2, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, -8, 4, -4, -2, 4, 4, 0, 0, 0, 0, 0, -4, -2, 2, 4, -4, 4, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 4, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663361
    {'cdim': 4, 'counter': 53, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4m', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 8, 2, -4, -4, 2, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, -8, -4, 4, -2, 4, 4, 0, 0, 0, 0, 0, -4, -2, 2, -4, 4, 4, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, 4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663362
    {'cdim': 4, 'counter': 54, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.4n', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -8, 8, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 4, 4, 0, 0, 4, 4, 4, -4, 4, -4, 4, 0, -4, 4, -4, 0, 0, -2, 0, -4, 4, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663385
    {'cdim': 8, 'counter': 75, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 2, 2, -4, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663386
    {'cdim': 8, 'counter': 76, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8b', 'multiplicity': 1, 'nt': [24, 678], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -8, 8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, -4, 2, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -2, 4, 0, 0, -2, 4, -2, -2, 2, 4, -4, 0, 2, -2, 2, 0, 0, 1, 0, -2, 2, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663387
    {'cdim': 8, 'counter': 77, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8c', 'multiplicity': 1, 'nt': [24, 678], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 8, -1, -4, 2, -1, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -2, -8, 4, -4, 1, 4, -2, 0, 0, 0, 0, 0, 2, 1, -1, -2, 2, -2, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663388
    {'cdim': 8, 'counter': 78, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8d', 'multiplicity': 1, 'nt': [24, 678], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 8, -1, -4, 2, -1, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -2, -8, -4, 4, 1, 4, -2, 0, 0, 0, 0, 0, 2, 1, -1, 2, -2, -2, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663389
    {'cdim': 8, 'counter': 79, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8e', 'multiplicity': 1, 'nt': [24, 678], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -8, 8, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, -4, 2, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -2, 4, 0, 0, -2, 4, -2, 2, -2, -4, 4, 0, 2, -2, 2, 0, 0, 1, 0, 2, -2, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663392
    {'cdim': 9, 'counter': 81, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9a', 'multiplicity': 1, 'nt': [16, 1033], 'qdim': 9, 'qvalues': [9, 9, 9, 9, -3, -3, 3, 3, -3, -3, 3, 3, 3, -1, 3, 1, -1, 1, 9, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, 1, -3, -1, 1, 1, -1, -1, 1, -1, 9, -3, -3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3, -3, 1, 1, -3, -3, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -3, -3, -3, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663393
    {'cdim': 9, 'counter': 82, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9b', 'multiplicity': 1, 'nt': [18, 181], 'qdim': 9, 'qvalues': [9, 9, 9, 9, -3, -3, -3, -3, -3, -3, -3, -3, -3, 1, -3, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, -3, 3, 3, -3, 3, 1, 3, 1, -1, 1, -1, 1, -1, -1, 9, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 3, -1, -1, 3, 3, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -3, 3, 3, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663394
    {'cdim': 9, 'counter': 83, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9c', 'multiplicity': 1, 'nt': [18, 187], 'qdim': 9, 'qvalues': [9, 9, 9, 9, -3, -3, -3, -3, -3, -3, 3, -3, -3, -1, 3, -1, -1, -1, 9, 0, 0, 0, 0, 0, 0, -3, 3, 3, -3, 3, 1, 3, 1, -1, 1, 1, 1, -1, 1, 9, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -3, -3, 1, 1, -3, -3, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -3, 3, 3, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663395
    {'cdim': 9, 'counter': 84, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9d', 'multiplicity': 1, 'nt': [18, 187], 'qdim': 9, 'qvalues': [9, 9, 9, 9, -3, -3, 3, 3, -3, -3, -3, 3, 3, 1, -3, -1, 1, -1, 9, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, 1, -3, -1, 1, 1, 1, -1, 1, 1, 9, -3, -3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 3, -1, -1, 3, 3, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -3, -3, -3, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663396
    {'cdim': 9, 'counter': 85, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9e', 'multiplicity': 1, 'nt': [18, 266], 'qdim': 9, 'qvalues': [9, 9, -9, -9, -3, -3, -3, -3, 3, 3, -3, 3, 3, 1, 3, 1, -1, -1, 9, 0, 0, 0, 0, 0, 0, -3, 3, 3, 3, -3, 1, -3, 1, -1, -1, -1, -1, 1, 1, 9, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 3, -1, -1, -3, -3, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -3, 3, 3, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663397
    {'cdim': 9, 'counter': 86, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9f', 'multiplicity': 1, 'nt': [18, 266], 'qdim': 9, 'qvalues': [9, 9, -9, -9, -3, -3, -3, -3, 3, 3, 3, 3, 3, -1, -3, -1, 1, 1, 9, 0, 0, 0, 0, 0, 0, -3, 3, 3, 3, -3, 1, -3, 1, -1, -1, 1, -1, 1, -1, 9, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -3, -3, 1, 1, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -3, 3, 3, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663398
    {'cdim': 9, 'counter': 87, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9g', 'multiplicity': 1, 'nt': [18, 266], 'qdim': 9, 'qvalues': [9, 9, -9, -9, -3, -3, 3, 3, 3, 3, -3, -3, -3, 1, 3, -1, -1, 1, 9, 0, 0, 0, 0, 0, 0, -3, -3, -3, 3, 3, 1, 3, -1, 1, -1, 1, 1, -1, -1, 9, -3, -3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 3, -1, -1, -3, -3, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -3, -3, -3, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663399
    {'cdim': 9, 'counter': 88, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.9h', 'multiplicity': 1, 'nt': [18, 266], 'qdim': 9, 'qvalues': [9, 9, -9, -9, -3, -3, 3, 3, 3, 3, 3, -3, -3, -1, -3, 1, 1, -1, 9, 0, 0, 0, 0, 0, 0, -3, -3, -3, 3, 3, 1, 3, -1, 1, -1, -1, 1, -1, 1, 9, -3, -3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3, -3, 1, 1, 3, 3, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -3, -3, -3, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663381
    {'cdim': 6, 'counter': 71, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6q', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 4, -4, -4, 4, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 12, -6, 0, -6, 0, 0, 0, 0, 4, -4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, 6, 0, -4, 4, 6, 0, -2, 6, -6, 0, 0, 0, 2, -2, 2, 2, -2, 0, 0, -2, 2, 0, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663382
    {'cdim': 6, 'counter': 72, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6r', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 4, -4, 4, -4, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 12, -6, 0, -6, 0, 0, 0, 0, -4, 4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, 6, 0, 4, -4, 6, 0, -2, 6, -6, 0, 0, 0, 2, -2, 2, -2, 2, 0, 0, -2, 2, 0, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663383
    {'cdim': 6, 'counter': 73, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6s', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 4, -4, -4, 4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, 12, -6, 0, -6, 0, 0, 0, 0, 4, -4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, 6, 0, -4, 4, 6, 0, -2, -6, 6, 0, 0, 0, 2, -2, 2, 2, -2, 0, 0, 2, -2, 0, -2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663384
    {'cdim': 6, 'counter': 74, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.6t', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 4, -4, 4, -4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, 12, -6, 0, -6, 0, 0, 0, 0, -4, 4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, 6, 0, 4, -4, 6, 0, -2, -6, 6, 0, 0, 0, 2, -2, 2, -2, 2, 0, 0, 2, -2, 0, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663400
    {'cdim': 12, 'counter': 89, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12a', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 3, 0, 0, 0, 12, -4, -4, 0, 0, -4, 0, 4, -4, 0, 0, 0, 0, 0, -6, 2, 2, -6, 0, -2, -2, 3, 0, 2, 0, 0, 0, 0, 0, 2, -1, -1, -2, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 2, 2, 2, 2, 0, -2, 2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663402
    {'cdim': 12, 'counter': 90, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12b', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 12, 12, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -6, 0, -6, 0, 3, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16663403
    {'cdim': 12, 'counter': 91, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12c', 'multiplicity': 1, 'nt': [24, 2698], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 4, -4, -4, 4, 4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 12, 3, 0, 3, 0, 0, 0, 0, 4, -4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, -3, 0, -4, 4, -3, 0, 1, -3, 3, 0, 0, 0, -1, 1, -1, -1, 1, 0, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663404
    {'cdim': 12, 'counter': 92, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12d', 'multiplicity': 1, 'nt': [24, 2698], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 4, -4, 4, -4, 4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 12, 3, 0, 3, 0, 0, 0, 0, -4, 4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, -3, 0, 4, -4, -3, 0, 1, -3, 3, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663405
    {'cdim': 12, 'counter': 93, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12e', 'multiplicity': 1, 'nt': [24, 2698], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 4, -4, -4, 4, -4, 4, 0, -4, 4, 0, 0, 0, 0, 0, 12, 3, 0, 3, 0, 0, 0, 0, 4, -4, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, -3, 0, -4, 4, -3, 0, 1, 3, -3, 0, 0, 0, -1, 1, -1, -1, 1, 0, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663406
    {'cdim': 12, 'counter': 94, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12f', 'multiplicity': 1, 'nt': [24, 2698], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 4, -4, 4, -4, -4, 4, 0, 4, -4, 0, 0, 0, 0, 0, 12, 3, 0, 3, 0, 0, 0, 0, -4, 4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, -4, 4, -3, 0, 4, -4, -3, 0, 1, 3, -3, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663407
    {'cdim': 12, 'counter': 95, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12g', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 3, 0, 0, 0, 12, 4, 4, 0, 0, -4, 0, -4, 4, 0, 0, 0, 0, 0, -6, 2, 2, -6, 0, 2, 2, 3, 0, 2, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2, -2, 2, -2, -2, 0, 2, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663408
    {'cdim': 12, 'counter': 96, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12h', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 12, 12, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -6, 0, -6, 0, 3, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16663391
    {'cdim': 8, 'counter': 80, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.8f', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 8, 8, 0, 0, -4, -4, 8, 0, 0, 0, 0, 0, -8, -4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663411
    {'cdim': 16, 'counter': 99, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.16a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, -8, -2, 4, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -4, 8, 0, 0, 2, -4, -4, 0, 0, 0, 0, 0, 4, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663309
    {'cdim': 18, 'counter': 100, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.18a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, 6, 6, 0, 0, 6, 0, 0, -2, 0, 2, 0, 0, -9, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, 2, 0, -2, 2, 0, -2, 0, 0, 0, -9, 3, 3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -6, -6, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 3, 3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663310
    {'cdim': 18, 'counter': 101, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.18b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, -6, -6, 0, 0, -6, 0, 0, 2, 0, 2, 0, 0, -9, 0, 0, 0, 0, 0, 0, -6, 6, 6, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, -9, 3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 6, 6, -2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 3, -3, -3, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, -3, -3, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663311
    {'cdim': 18, 'counter': 102, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.18c', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, -6, -6, 0, 0, 6, 0, 0, -2, 0, -2, 0, 0, -9, 0, 0, 0, 0, 0, 0, -6, 6, 6, 0, 0, 2, 0, 2, -2, 0, 2, 0, 0, 0, -9, 3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -6, -6, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 3, -3, -3, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 3, 3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663312
    {'cdim': 18, 'counter': 103, 'faithful': False, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.18d', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, 6, 6, 0, 0, -6, 0, 0, 2, 0, -2, 0, 0, -9, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, 2, 0, -2, 2, 0, 2, 0, 0, 0, -9, 3, 3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 6, -2, -2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 3, 3, 3, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, -3, -3, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663409
    {'cdim': 12, 'counter': 97, 'faithful': True, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12i', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, 6, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -4, 12, 0, 4, -4, -6, 0, -4, 0, 0, 0, 0, 0, 4, 2, -2, 4, -4, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, 4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663410
    {'cdim': 12, 'counter': 98, 'faithful': True, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.12j', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, 6, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -4, 12, 0, -4, 4, -6, 0, -4, 0, 0, 0, 0, 0, 4, 2, -2, -4, 4, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 4, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663313
    {'cdim': 24, 'counter': 104, 'faithful': True, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.24a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 0, -3, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -4, -6, 0, 4, -4, 3, 0, 2, 0, 0, 0, 0, 0, -2, -1, 1, -2, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16663314
    {'cdim': 24, 'counter': 105, 'faithful': True, 'group': '6912.ia', 'group_order': 6912, 'image': None, 'label': '6912.ia.24b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 0, -3, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -4, -6, 0, -4, 4, 3, 0, 2, 0, 0, 0, 0, 0, -2, -1, 1, 2, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 36902993
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 6912, 'label': '6912.ia.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903025
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903036
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903047
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903058
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903069
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903080
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903091
    {'center': None, 'center_index': 1, 'center_order': 6912, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '6912.ia.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903102
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 1152, 'label': '6912.ia.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902994
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 1152, 'label': '6912.ia.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903005
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 1152, 'label': '6912.ia.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903016
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903018
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903019
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903020
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903021
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903022
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903023
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903024
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903026
    {'center': None, 'center_index': 6, 'center_order': 1152, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 576, 'label': '6912.ia.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903027
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2m1', 'nt': [24, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903028
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2m2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903029
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 23, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2n1', 'nt': [24, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903030
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 24, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2n2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903031
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 25, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2o1', 'nt': [24, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903032
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 26, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2o2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903033
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 27, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2p1', 'nt': [24, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903034
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 28, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.2p2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903035
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 288, 'label': '6912.ia.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903037
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 288, 'label': '6912.ia.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903038
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 288, 'label': '6912.ia.3c', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903039
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 288, 'label': '6912.ia.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903040
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903041
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903042
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903043
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903044
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903045
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903046
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3k', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903048
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3l', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903049
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 41, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3m', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903050
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 42, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3n', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903051
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 43, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3o', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903052
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 44, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.3p', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903053
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': None, 'kernel_order': 192, 'label': '6912.ia.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903054
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': None, 'kernel_order': 192, 'label': '6912.ia.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903055
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': None, 'kernel_order': 192, 'label': '6912.ia.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903056
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.4d', 'nt': [8, 23], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903057
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.4e', 'nt': [8, 23], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903059
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.4f', 'nt': [8, 23], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903060
    {'center': None, 'center_index': 24, 'center_order': 288, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 144, 'label': '6912.ia.4g', 'nt': [8, 23], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903061
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 52, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 96, 'label': '6912.ia.4h', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903062
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 53, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 96, 'label': '6912.ia.4i', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903063
    {'center': None, 'center_index': 36, 'center_order': 192, 'counter': 54, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 96, 'label': '6912.ia.4j', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903064
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 55, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4k1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903065
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 56, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4k2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903066
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 57, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4l1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903067
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 58, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4l2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903068
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 59, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4m1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903070
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 60, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4m2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903071
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 61, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4n1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36903072
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 62, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 0, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.4n2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36903073
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 63, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6a', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[6, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903074
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 64, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6b', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903075
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 65, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6c', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903076
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 66, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6d', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903077
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 67, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6e', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[6, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903078
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 68, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6f', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903079
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 69, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6g', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903081
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 70, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 48, 'label': '6912.ia.6h', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903082
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 71, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6i', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903083
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 72, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6j', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903084
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 73, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6k', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36903085
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 74, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6l', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36903086
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 75, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6m', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[6, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903087
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 76, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6n', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[6, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903088
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 77, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6o', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903089
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 78, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.6p', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903090
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 79, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6q1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903092
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 80, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6q2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903093
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 81, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6r1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903094
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 82, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6r2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903095
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 83, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6s1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903096
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 84, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6s2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903097
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 85, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6t1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903098
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 86, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 0, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.6t2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903099
    {'center': None, 'center_index': 216, 'center_order': 32, 'counter': 87, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '216.162', 'image_order': 216, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6912.ia.8a', 'nt': [12, 117], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903100
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 88, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.8b', 'nt': [24, 678], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903101
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 89, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.8c', 'nt': [24, 678], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903103
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 90, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.8d', 'nt': [24, 678], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903104
    {'center': None, 'center_index': 144, 'center_order': 48, 'counter': 91, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 288, 'indicator': 1, 'kernel': None, 'kernel_order': 24, 'label': '6912.ia.8e', 'nt': [24, 678], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903105
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 92, 'cyclotomic_n': 8, 'dim': 8, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '1728.46336', 'image_order': 1728, 'indicator': 0, 'kernel': None, 'kernel_order': 4, 'label': '6912.ia.8f1', 'nt': [96, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, 3]], [[4, 1], [4, 3]], [[-4, 1], [-4, 3]], [[4, 1], [4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903106
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 93, 'cyclotomic_n': 8, 'dim': 8, 'faithful': False, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '1728.46336', 'image_order': 1728, 'indicator': 0, 'kernel': None, 'kernel_order': 4, 'label': '6912.ia.8f2', 'nt': [96, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, 3]], [[-4, 1], [-4, 3]], [[4, 1], [4, 3]], [[-4, 1], [-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 36903107
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 94, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 576, 'indicator': 1, 'kernel': None, 'kernel_order': 12, 'label': '6912.ia.9a', 'nt': [16, 1033], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903108
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 95, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 576, 'indicator': 1, 'kernel': None, 'kernel_order': 12, 'label': '6912.ia.9b', 'nt': [18, 181], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903109
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 96, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 576, 'indicator': 1, 'kernel': None, 'kernel_order': 12, 'label': '6912.ia.9c', 'nt': [18, 187], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903110
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 97, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 576, 'indicator': 1, 'kernel': None, 'kernel_order': 12, 'label': '6912.ia.9d', 'nt': [18, 187], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903111
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 98, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.9e', 'nt': [18, 266], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903112
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 99, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.9f', 'nt': [18, 266], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902995
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 100, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.9g', 'nt': [18, 266], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902996
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 101, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.9h', 'nt': [18, 266], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902997
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 102, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6912.ia.12a', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902998
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 103, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6912.ia.12b', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36902999
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 104, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.12c', 'nt': [24, 2698], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903000
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 105, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.12d', 'nt': [24, 2698], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903001
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 106, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.12e', 'nt': [24, 2698], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903002
    {'center': None, 'center_index': 576, 'center_order': 12, 'counter': 107, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': None, 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 6, 'label': '6912.ia.12f', 'nt': [24, 2698], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903003
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 108, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6912.ia.12g', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903004
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 109, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6912.ia.12h', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903006
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 110, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.12i1', 'nt': [144, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, 3]], [[6, 1], [6, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903007
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 111, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.12i2', 'nt': [144, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, 3]], [[-6, 1], [-6, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903008
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 112, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.12j1', 'nt': [144, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, 3]], [[6, 1], [6, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903009
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 113, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.12j2', 'nt': [144, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, 3]], [[-6, 1], [-6, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903010
    {'center': None, 'center_index': 864, 'center_order': 8, 'counter': 114, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '1728.46336', 'image_order': 1728, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '6912.ia.16a', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903011
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 115, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '3456.jo', 'image_order': 3456, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6912.ia.18a', 'nt': [48, 0], 'q_character': None, 'values': [[[18, 0]], [[18, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903012
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 116, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '3456.jo', 'image_order': 3456, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6912.ia.18b', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[18, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903013
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 117, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '3456.jo', 'image_order': 3456, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6912.ia.18c', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[18, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903014
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 118, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '3456.jo', 'image_order': 3456, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6912.ia.18d', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[18, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903015
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 119, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.24a', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36903017
    {'center': None, 'center_index': 3456, 'center_order': 2, 'counter': 120, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '6912.ia', 'group_counter': 209, 'group_order': 6912, 'image': None, 'image_isoclass': '6912.ia', 'image_order': 6912, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6912.ia.24b', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 243564561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6912, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '6912.ia.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6912.ia', 'subgroup_hash': 4930085545709402789, 'subgroup_order': 6912, 'subgroup_tex': 'D_6.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.pt', 'subgroup_hash': 4533135310382536022, 'subgroup_order': 3456, 'subgroup_tex': 'S_3\\times S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.ne', 'subgroup_hash': 601826204043287647, 'subgroup_order': 3456, 'subgroup_tex': 'S_3\\times A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.qd', 'subgroup_hash': 8583683500574977436, 'subgroup_order': 3456, 'subgroup_tex': 'S_3\\times A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 3456, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.qe', 'subgroup_hash': 7082449280128199437, 'subgroup_order': 3456, 'subgroup_tex': 'C_6.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.lw', 'subgroup_hash': 5445305980054046356, 'subgroup_order': 3456, 'subgroup_tex': 'C_6.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.nk', 'subgroup_hash': 3529763636164363181, 'subgroup_order': 3456, 'subgroup_tex': 'C_6.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243568015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3456, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.nj', 'subgroup_hash': 6244727894380608069, 'subgroup_order': 3456, 'subgroup_tex': 'C_6.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243568126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1152, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2304.d', 'subgroup_hash': 8112084019139883741, 'subgroup_order': 2304, 'subgroup_tex': 'C_2^2.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243564562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1152, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2304.ti', 'subgroup_hash': 4174976724645738920, 'subgroup_order': 2304, 'subgroup_tex': 'S_3\\times D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1152, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.3.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2304.ou', 'subgroup_hash': 5095203593532868286, 'subgroup_order': 2304, 'subgroup_tex': 'S_3\\times \\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1728, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46407', 'subgroup_hash': 46407, 'subgroup_order': 1728, 'subgroup_tex': 'D_6.A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243564895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1728, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46378', 'subgroup_hash': 46378, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1728, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46379', 'subgroup_hash': 46379, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1728, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46385', 'subgroup_hash': 46385, 'subgroup_order': 1728, 'subgroup_tex': 'C_3:S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1728, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46386', 'subgroup_hash': 46386, 'subgroup_order': 1728, 'subgroup_tex': 'A_4\\times C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1728, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46397', 'subgroup_hash': 46397, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1728, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46402', 'subgroup_hash': 46402, 'subgroup_order': 1728, 'subgroup_tex': '(C_3\\times A_4):\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.4.h1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47874', 'subgroup_hash': 47874, 'subgroup_order': 1728, 'subgroup_tex': 'A_4:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.4.i1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46336', 'subgroup_hash': 46336, 'subgroup_order': 1728, 'subgroup_tex': 'S_3^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1152, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157583', 'subgroup_hash': 914279088263562664, 'subgroup_order': 1152, 'subgroup_tex': 'C_2^3.D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1152, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157579', 'subgroup_hash': 7167418868790813737, 'subgroup_order': 1152, 'subgroup_tex': 'Q_8:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243566006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 1152, 'counter': 23, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157489', 'subgroup_hash': 679370211668863458, 'subgroup_order': 1152, 'subgroup_tex': 'C_2\\times S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157490', 'subgroup_hash': 3961218714212941200, 'subgroup_order': 1152, 'subgroup_tex': 'C_2\\times A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157522', 'subgroup_hash': 701453766061161572, 'subgroup_order': 1152, 'subgroup_tex': 'C_2\\times A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 288, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157579', 'subgroup_hash': 7167418868790813737, 'subgroup_order': 1152, 'subgroup_tex': 'Q_8:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243566561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156260', 'subgroup_hash': 8482679216537043163, 'subgroup_order': 1152, 'subgroup_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243566672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 288, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155774', 'subgroup_hash': 7604470634633290792, 'subgroup_order': 1152, 'subgroup_tex': 'C_4\\times S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155775', 'subgroup_hash': 4492155018186357460, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157270', 'subgroup_hash': 6217908760980627513, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157559', 'subgroup_hash': 1937509066773009460, 'subgroup_order': 1152, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 288, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155795', 'subgroup_hash': 4047434960502163306, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156064', 'subgroup_hash': 6446418664246003612, 'subgroup_order': 1152, 'subgroup_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157334', 'subgroup_hash': 4196427323472421323, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156260', 'subgroup_hash': 8482679216537043163, 'subgroup_order': 1152, 'subgroup_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155799', 'subgroup_hash': 7082498570119804226, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156189', 'subgroup_hash': 4525101610896267624, 'subgroup_order': 1152, 'subgroup_tex': 'D_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157649', 'subgroup_hash': 152108753463096738, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156261', 'subgroup_hash': 2927393297673880901, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156262', 'subgroup_hash': 168640125157868536, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:(D_4\\times \\GL(2,3))', 'supersolvable': False, 'sylow': 0}
  • id: 243567594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155776', 'subgroup_hash': 6491415882587411929, 'subgroup_order': 1152, 'subgroup_tex': 'D_{12}\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155777', 'subgroup_hash': 1801734664593410413, 'subgroup_order': 1152, 'subgroup_tex': 'D_{12}:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 576, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156692', 'subgroup_hash': 3236653830301820738, 'subgroup_order': 1152, 'subgroup_tex': 'C_3\\times D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156957', 'subgroup_hash': 3725352468715308951, 'subgroup_order': 1152, 'subgroup_tex': 'D_4\\times C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156080', 'subgroup_hash': 6668399606727010383, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 576, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156754', 'subgroup_hash': 8712613577892574515, 'subgroup_order': 1152, 'subgroup_tex': 'C_3\\times \\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155810', 'subgroup_hash': 4381494738345161381, 'subgroup_order': 1152, 'subgroup_tex': 'C_{24}:C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156208', 'subgroup_hash': 5251437388611204826, 'subgroup_order': 1152, 'subgroup_tex': 'Q_8:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156082', 'subgroup_hash': 4959286728109998662, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:(\\SD_{16}\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157019', 'subgroup_hash': 516451506675371807, 'subgroup_order': 1152, 'subgroup_tex': 'C_{24}:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156261', 'subgroup_hash': 2927393297673880901, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157461', 'subgroup_hash': 7371672288863537087, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156262', 'subgroup_hash': 168640125157868536, 'subgroup_order': 1152, 'subgroup_tex': 'C_3:(D_4\\times \\GL(2,3))', 'supersolvable': False, 'sylow': 0}
  • id: 243567782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155814', 'subgroup_hash': 1125878047224513635, 'subgroup_order': 1152, 'subgroup_tex': 'C_{24}:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.6.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.156210', 'subgroup_hash': 566743201714047859, 'subgroup_order': 1152, 'subgroup_tex': 'Q_8:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 864, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4195', 'subgroup_hash': 4195, 'subgroup_order': 864, 'subgroup_tex': 'C_6.A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4694', 'subgroup_hash': 4694, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4692', 'subgroup_hash': 4692, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4189', 'subgroup_hash': 4189, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4135', 'subgroup_hash': 4135, 'subgroup_order': 864, 'subgroup_tex': 'C_3\\times S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4165', 'subgroup_hash': 4165, 'subgroup_order': 864, 'subgroup_tex': '\\SL(2,3):S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4691', 'subgroup_hash': 4691, 'subgroup_order': 864, 'subgroup_tex': 'C_6:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4692', 'subgroup_hash': 4692, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4693', 'subgroup_hash': 4693, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4135', 'subgroup_hash': 4135, 'subgroup_order': 864, 'subgroup_tex': 'C_3\\times S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4165', 'subgroup_hash': 4165, 'subgroup_order': 864, 'subgroup_tex': '\\SL(2,3):S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4150', 'subgroup_hash': 4150, 'subgroup_order': 864, 'subgroup_tex': 'C_3:S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4178', 'subgroup_hash': 4178, 'subgroup_order': 864, 'subgroup_tex': '\\SL(2,3):S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 192, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1089273', 'subgroup_hash': 1089273, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\times D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1089272', 'subgroup_hash': 1089272, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\times \\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1044776', 'subgroup_hash': 1044776, 'subgroup_order': 768, 'subgroup_tex': 'D_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 576, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8496', 'subgroup_hash': 8496, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8498', 'subgroup_hash': 8498, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8442', 'subgroup_hash': 8442, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 576, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8272', 'subgroup_hash': 8272, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 576, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8440', 'subgroup_hash': 8440, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 576, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8271', 'subgroup_hash': 8271, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8463', 'subgroup_hash': 8463, 'subgroup_order': 576, 'subgroup_tex': 'Q_8\\times C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 576, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8461', 'subgroup_hash': 8461, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 576, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8280', 'subgroup_hash': 8280, 'subgroup_order': 576, 'subgroup_tex': 'A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243568127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8357', 'subgroup_hash': 8357, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2.A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 243568138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8496', 'subgroup_hash': 8496, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 288, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5558', 'subgroup_hash': 5558, 'subgroup_order': 576, 'subgroup_tex': 'C_4\\times S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5098', 'subgroup_hash': 5098, 'subgroup_order': 576, 'subgroup_tex': 'D_6.\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8553', 'subgroup_hash': 8553, 'subgroup_order': 576, 'subgroup_tex': 'C_4:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243564563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 288, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8311', 'subgroup_hash': 8311, 'subgroup_order': 576, 'subgroup_tex': 'C_4\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8353', 'subgroup_hash': 8353, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8493', 'subgroup_hash': 8493, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8312', 'subgroup_hash': 8312, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8305', 'subgroup_hash': 8305, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5568', 'subgroup_hash': 5568, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5063', 'subgroup_hash': 5063, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8511', 'subgroup_hash': 8511, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 288, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.6620', 'subgroup_hash': 6620, 'subgroup_order': 576, 'subgroup_tex': '\\SD_{16}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243564685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5591', 'subgroup_hash': 5591, 'subgroup_order': 576, 'subgroup_tex': 'C_3:D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8440', 'subgroup_hash': 8440, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5489', 'subgroup_hash': 5489, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8461', 'subgroup_hash': 8461, 'subgroup_order': 576, 'subgroup_tex': 'C_2\\times C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5537', 'subgroup_hash': 5537, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5559', 'subgroup_hash': 5559, 'subgroup_order': 576, 'subgroup_tex': 'D_{12}\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5099', 'subgroup_hash': 5099, 'subgroup_order': 576, 'subgroup_tex': 'D_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5100', 'subgroup_hash': 5100, 'subgroup_order': 576, 'subgroup_tex': 'D_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5460', 'subgroup_hash': 5460, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5095', 'subgroup_hash': 5095, 'subgroup_order': 576, 'subgroup_tex': 'C_3:C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5099', 'subgroup_hash': 5099, 'subgroup_order': 576, 'subgroup_tex': 'D_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5100', 'subgroup_hash': 5100, 'subgroup_order': 576, 'subgroup_tex': 'D_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5461', 'subgroup_hash': 5461, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5097', 'subgroup_hash': 5097, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times \\GL(2,3)):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 243564884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5508', 'subgroup_hash': 5508, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5096', 'subgroup_hash': 5096, 'subgroup_order': 576, 'subgroup_tex': 'C_3:(C_4\\times \\GL(2,3))', 'supersolvable': False, 'sylow': 0}
  • id: 243564907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5097', 'subgroup_hash': 5097, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times \\GL(2,3)):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 243564918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5509', 'subgroup_hash': 5509, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 288, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7424', 'subgroup_hash': 7424, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8354', 'subgroup_hash': 8354, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243564951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8437', 'subgroup_hash': 8437, 'subgroup_order': 576, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243564962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8313', 'subgroup_hash': 8313, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243564973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8301', 'subgroup_hash': 8301, 'subgroup_order': 576, 'subgroup_tex': 'C_3:Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5467', 'subgroup_hash': 5467, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5055', 'subgroup_hash': 5055, 'subgroup_order': 576, 'subgroup_tex': 'C_3:C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 192, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8272', 'subgroup_hash': 8272, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8355', 'subgroup_hash': 8355, 'subgroup_order': 576, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 243565029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8458', 'subgroup_hash': 8458, 'subgroup_order': 576, 'subgroup_tex': 'D_4\\times C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5585', 'subgroup_hash': 5585, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times C_3:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243565051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5482', 'subgroup_hash': 5482, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5530', 'subgroup_hash': 5530, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7435', 'subgroup_hash': 7435, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243565084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 192, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8271', 'subgroup_hash': 8271, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5591', 'subgroup_hash': 5591, 'subgroup_order': 576, 'subgroup_tex': 'C_3:D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8272', 'subgroup_hash': 8272, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8272', 'subgroup_hash': 8272, 'subgroup_order': 576, 'subgroup_tex': 'S_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8314', 'subgroup_hash': 8314, 'subgroup_order': 576, 'subgroup_tex': 'D_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8304', 'subgroup_hash': 8304, 'subgroup_order': 576, 'subgroup_tex': 'C_3:(Q_8\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5515', 'subgroup_hash': 5515, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5056', 'subgroup_hash': 5056, 'subgroup_order': 576, 'subgroup_tex': 'C_3:(C_8\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5570', 'subgroup_hash': 5570, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times C_{24}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 243565184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5067', 'subgroup_hash': 5067, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5068', 'subgroup_hash': 5068, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5586', 'subgroup_hash': 5586, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times Q_8:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 243565217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8271', 'subgroup_hash': 8271, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8271', 'subgroup_hash': 8271, 'subgroup_order': 576, 'subgroup_tex': 'A_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 288, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5489', 'subgroup_hash': 5489, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5069', 'subgroup_hash': 5069, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5469', 'subgroup_hash': 5469, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5059', 'subgroup_hash': 5059, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5485', 'subgroup_hash': 5485, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8476', 'subgroup_hash': 8476, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5537', 'subgroup_hash': 5537, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5070', 'subgroup_hash': 5070, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5060', 'subgroup_hash': 5060, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5517', 'subgroup_hash': 5517, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5533', 'subgroup_hash': 5533, 'subgroup_order': 576, 'subgroup_tex': 'C_6.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8483', 'subgroup_hash': 8483, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_6):\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8280', 'subgroup_hash': 8280, 'subgroup_order': 576, 'subgroup_tex': 'A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8280', 'subgroup_hash': 8280, 'subgroup_order': 576, 'subgroup_tex': 'A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8280', 'subgroup_hash': 8280, 'subgroup_order': 576, 'subgroup_tex': 'A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8280', 'subgroup_hash': 8280, 'subgroup_order': 576, 'subgroup_tex': 'A_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.12.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8325', 'subgroup_hash': 8325, 'subgroup_order': 576, 'subgroup_tex': 'D_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.623', 'subgroup_hash': 623, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 144, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.762', 'subgroup_hash': 762, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.623', 'subgroup_hash': 623, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 144, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.614', 'subgroup_hash': 614, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.626', 'subgroup_hash': 626, 'subgroup_order': 432, 'subgroup_tex': 'C_3:S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.617', 'subgroup_hash': 617, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.617', 'subgroup_hash': 617, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.620', 'subgroup_hash': 620, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243565661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.16.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20055', 'subgroup_hash': 20055, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18081', 'subgroup_hash': 18081, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17899', 'subgroup_hash': 17899, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17900', 'subgroup_hash': 17900, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18171', 'subgroup_hash': 18171, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20051', 'subgroup_hash': 20051, 'subgroup_order': 384, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 243565751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18011', 'subgroup_hash': 18011, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20057', 'subgroup_hash': 20057, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18063', 'subgroup_hash': 18063, 'subgroup_order': 384, 'subgroup_tex': 'C_4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18207', 'subgroup_hash': 18207, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\times A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243565796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 192, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20055', 'subgroup_hash': 20055, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18081', 'subgroup_hash': 18081, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18014', 'subgroup_hash': 18014, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243565829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18074', 'subgroup_hash': 18074, 'subgroup_order': 384, 'subgroup_tex': 'C_4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243565840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20082', 'subgroup_hash': 20082, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12720', 'subgroup_hash': 12720, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.19749', 'subgroup_hash': 19749, 'subgroup_order': 384, 'subgroup_tex': 'C_{24}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243565873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13231', 'subgroup_hash': 13231, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12613', 'subgroup_hash': 12613, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13002', 'subgroup_hash': 13002, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12219', 'subgroup_hash': 12219, 'subgroup_order': 384, 'subgroup_tex': 'C_4\\times S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.14335', 'subgroup_hash': 14335, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12957', 'subgroup_hash': 12957, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.19195', 'subgroup_hash': 19195, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.11996', 'subgroup_hash': 11996, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.19334', 'subgroup_hash': 19334, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12720', 'subgroup_hash': 12720, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 192, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.19749', 'subgroup_hash': 19749, 'subgroup_order': 384, 'subgroup_tex': 'C_{24}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243565995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13231', 'subgroup_hash': 13231, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12613', 'subgroup_hash': 12613, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12747', 'subgroup_hash': 12747, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.16441', 'subgroup_hash': 16441, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13252', 'subgroup_hash': 13252, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12639', 'subgroup_hash': 12639, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13024', 'subgroup_hash': 13024, 'subgroup_order': 384, 'subgroup_tex': 'D_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12249', 'subgroup_hash': 12249, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.14347', 'subgroup_hash': 14347, 'subgroup_order': 384, 'subgroup_tex': 'D_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12982', 'subgroup_hash': 12982, 'subgroup_order': 384, 'subgroup_tex': 'D_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.16069', 'subgroup_hash': 16069, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17721', 'subgroup_hash': 17721, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 192, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12010', 'subgroup_hash': 12010, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.16137', 'subgroup_hash': 16137, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 192, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12747', 'subgroup_hash': 12747, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.16441', 'subgroup_hash': 16441, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 192, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17972', 'subgroup_hash': 17972, 'subgroup_order': 384, 'subgroup_tex': 'D_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18035', 'subgroup_hash': 18035, 'subgroup_order': 384, 'subgroup_tex': '\\SD_{16}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13252', 'subgroup_hash': 13252, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.18.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12639', 'subgroup_hash': 12639, 'subgroup_order': 384, 'subgroup_tex': 'C_6.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 288, 'counter': 265, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 288, 'counter': 266, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 288, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.981', 'subgroup_hash': 981, 'subgroup_order': 288, 'subgroup_tex': 'Q_8:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243566428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.982', 'subgroup_hash': 982, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243566439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 288, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.859', 'subgroup_hash': 859, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243566473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243566584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243566595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.919', 'subgroup_hash': 919, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.437', 'subgroup_hash': 437, 'subgroup_order': 288, 'subgroup_tex': 'C_8\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.965', 'subgroup_hash': 965, 'subgroup_order': 288, 'subgroup_tex': 'Q_8\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.576', 'subgroup_hash': 576, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.684', 'subgroup_hash': 684, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.440', 'subgroup_hash': 440, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.586', 'subgroup_hash': 586, 'subgroup_order': 288, 'subgroup_tex': 'Q_8:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.981', 'subgroup_hash': 981, 'subgroup_order': 288, 'subgroup_tex': 'Q_8:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243566829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.952', 'subgroup_hash': 952, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 144, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.633', 'subgroup_hash': 633, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.409', 'subgroup_hash': 409, 'subgroup_order': 288, 'subgroup_tex': 'C_3:C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.399', 'subgroup_hash': 399, 'subgroup_order': 288, 'subgroup_tex': '\\SL(2,3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243566973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.403', 'subgroup_hash': 403, 'subgroup_order': 288, 'subgroup_tex': 'C_6.\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243566995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.897', 'subgroup_hash': 897, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.853', 'subgroup_hash': 853, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.928', 'subgroup_hash': 928, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.906', 'subgroup_hash': 906, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.917', 'subgroup_hash': 917, 'subgroup_order': 288, 'subgroup_tex': 'C_3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.980', 'subgroup_hash': 980, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.908', 'subgroup_hash': 908, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.854', 'subgroup_hash': 854, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.857', 'subgroup_hash': 857, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.858', 'subgroup_hash': 858, 'subgroup_order': 288, 'subgroup_tex': 'D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.920', 'subgroup_hash': 920, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243567262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.855', 'subgroup_hash': 855, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.898', 'subgroup_hash': 898, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.909', 'subgroup_hash': 909, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.918', 'subgroup_hash': 918, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243567306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.896', 'subgroup_hash': 896, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.907', 'subgroup_hash': 907, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.637', 'subgroup_hash': 637, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 243567340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.408', 'subgroup_hash': 408, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243567351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.398', 'subgroup_hash': 398, 'subgroup_order': 288, 'subgroup_tex': 'A_4:C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 243567362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.402', 'subgroup_hash': 402, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.852', 'subgroup_hash': 852, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.986', 'subgroup_hash': 986, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.859', 'subgroup_hash': 859, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.859', 'subgroup_hash': 859, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.859', 'subgroup_hash': 859, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.922', 'subgroup_hash': 922, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.900', 'subgroup_hash': 900, 'subgroup_order': 288, 'subgroup_tex': 'C_6\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.911', 'subgroup_hash': 911, 'subgroup_order': 288, 'subgroup_tex': 'C_6:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.576', 'subgroup_hash': 576, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.684', 'subgroup_hash': 684, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.440', 'subgroup_hash': 440, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.586', 'subgroup_hash': 586, 'subgroup_order': 288, 'subgroup_tex': 'Q_8:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.578', 'subgroup_hash': 578, 'subgroup_order': 288, 'subgroup_tex': 'D_4.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.770', 'subgroup_hash': 770, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.851', 'subgroup_hash': 851, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.444', 'subgroup_hash': 444, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.588', 'subgroup_hash': 588, 'subgroup_order': 288, 'subgroup_tex': 'Q_8:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.24.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '6912.ia.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54029', 'subgroup_hash': 54029, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 2}
  • id: 243567561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.134', 'subgroup_hash': 134, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 407, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1517', 'subgroup_hash': 1517, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 192, 'counter': 408, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1477', 'subgroup_hash': 1477, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 192, 'counter': 409, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1498', 'subgroup_hash': 1498, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.996', 'subgroup_hash': 996, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.977', 'subgroup_hash': 977, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1469', 'subgroup_hash': 1469, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243567595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1470', 'subgroup_hash': 1470, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243567597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 96, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1498', 'subgroup_hash': 1498, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1468', 'subgroup_hash': 1468, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1010', 'subgroup_hash': 1010, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 243567600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.967', 'subgroup_hash': 967, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243567601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1499', 'subgroup_hash': 1499, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1506', 'subgroup_hash': 1506, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1163', 'subgroup_hash': 1163, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1295', 'subgroup_hash': 1295, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.283', 'subgroup_hash': 283, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1185', 'subgroup_hash': 1185, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1517', 'subgroup_hash': 1517, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1163', 'subgroup_hash': 1163, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1103', 'subgroup_hash': 1103, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1273', 'subgroup_hash': 1273, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.243', 'subgroup_hash': 243, 'subgroup_order': 192, 'subgroup_tex': 'D_6.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.391', 'subgroup_hash': 391, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1282', 'subgroup_hash': 1282, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.418', 'subgroup_hash': 418, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.360', 'subgroup_hash': 360, 'subgroup_order': 192, 'subgroup_tex': 'D_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.360', 'subgroup_hash': 360, 'subgroup_order': 192, 'subgroup_tex': 'D_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1130', 'subgroup_hash': 1130, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.360', 'subgroup_hash': 360, 'subgroup_order': 192, 'subgroup_tex': 'D_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1103', 'subgroup_hash': 1103, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1163', 'subgroup_hash': 1163, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1185', 'subgroup_hash': 1185, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1295', 'subgroup_hash': 1295, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.283', 'subgroup_hash': 283, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1004', 'subgroup_hash': 1004, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1149', 'subgroup_hash': 1149, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1360', 'subgroup_hash': 1360, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1168', 'subgroup_hash': 1168, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1191', 'subgroup_hash': 1191, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(D_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 243567658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.668', 'subgroup_hash': 668, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.284', 'subgroup_hash': 284, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(C_8\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1374', 'subgroup_hash': 1374, 'subgroup_order': 192, 'subgroup_tex': 'C_3:D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1353', 'subgroup_hash': 1353, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.777', 'subgroup_hash': 777, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.883', 'subgroup_hash': 883, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1459', 'subgroup_hash': 1459, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.599', 'subgroup_hash': 599, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.600', 'subgroup_hash': 600, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.898', 'subgroup_hash': 898, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.881', 'subgroup_hash': 881, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1298', 'subgroup_hash': 1298, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.290', 'subgroup_hash': 290, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.605', 'subgroup_hash': 605, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1366', 'subgroup_hash': 1366, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.297', 'subgroup_hash': 297, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.673', 'subgroup_hash': 673, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.607', 'subgroup_hash': 607, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.786', 'subgroup_hash': 786, 'subgroup_order': 192, 'subgroup_tex': '(C_3\\times Q_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1004', 'subgroup_hash': 1004, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1168', 'subgroup_hash': 1168, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1108', 'subgroup_hash': 1108, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1276', 'subgroup_hash': 1276, 'subgroup_order': 192, 'subgroup_tex': 'C_3:D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1286', 'subgroup_hash': 1286, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.245', 'subgroup_hash': 245, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.393', 'subgroup_hash': 393, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1134', 'subgroup_hash': 1134, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.729', 'subgroup_hash': 729, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.337', 'subgroup_hash': 337, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.730', 'subgroup_hash': 730, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.729', 'subgroup_hash': 729, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.365', 'subgroup_hash': 365, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.423', 'subgroup_hash': 423, 'subgroup_order': 192, 'subgroup_tex': 'C_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.366', 'subgroup_hash': 366, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.365', 'subgroup_hash': 365, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.576', 'subgroup_hash': 576, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.578', 'subgroup_hash': 578, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.894', 'subgroup_hash': 894, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.317', 'subgroup_hash': 317, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(C_4\\times \\SD_{16})', 'supersolvable': True, 'sylow': 0}
  • id: 243567726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.721', 'subgroup_hash': 721, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.721', 'subgroup_hash': 721, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.871', 'subgroup_hash': 871, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.720', 'subgroup_hash': 720, 'subgroup_order': 192, 'subgroup_tex': 'C_3:C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.729', 'subgroup_hash': 729, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.337', 'subgroup_hash': 337, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.730', 'subgroup_hash': 730, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.729', 'subgroup_hash': 729, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.335', 'subgroup_hash': 335, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.365', 'subgroup_hash': 365, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.423', 'subgroup_hash': 423, 'subgroup_order': 192, 'subgroup_tex': 'C_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.366', 'subgroup_hash': 366, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.365', 'subgroup_hash': 365, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.634', 'subgroup_hash': 634, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.635', 'subgroup_hash': 635, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.925', 'subgroup_hash': 925, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.893', 'subgroup_hash': 893, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.321', 'subgroup_hash': 321, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.734', 'subgroup_hash': 734, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.734', 'subgroup_hash': 734, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.722', 'subgroup_hash': 722, 'subgroup_order': 192, 'subgroup_tex': '(C_3\\times Q_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.952', 'subgroup_hash': 952, 'subgroup_order': 192, 'subgroup_tex': 'C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.952', 'subgroup_hash': 952, 'subgroup_order': 192, 'subgroup_tex': 'C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.250', 'subgroup_hash': 250, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.400', 'subgroup_hash': 400, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.642', 'subgroup_hash': 642, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.411', 'subgroup_hash': 411, 'subgroup_order': 192, 'subgroup_tex': 'C_8:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 243567766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.377', 'subgroup_hash': 377, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.377', 'subgroup_hash': 377, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.584', 'subgroup_hash': 584, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.347', 'subgroup_hash': 347, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 243567770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.321', 'subgroup_hash': 321, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.734', 'subgroup_hash': 734, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.734', 'subgroup_hash': 734, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.722', 'subgroup_hash': 722, 'subgroup_order': 192, 'subgroup_tex': '(C_3\\times Q_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.952', 'subgroup_hash': 952, 'subgroup_order': 192, 'subgroup_tex': 'C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.407', 'subgroup_hash': 407, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.252', 'subgroup_hash': 252, 'subgroup_order': 192, 'subgroup_tex': 'C_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.644', 'subgroup_hash': 644, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.586', 'subgroup_hash': 586, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.952', 'subgroup_hash': 952, 'subgroup_order': 192, 'subgroup_tex': 'C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.952', 'subgroup_hash': 952, 'subgroup_order': 192, 'subgroup_tex': 'C_4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1360', 'subgroup_hash': 1360, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1434', 'subgroup_hash': 1434, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1108', 'subgroup_hash': 1108, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1096', 'subgroup_hash': 1096, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.867', 'subgroup_hash': 867, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243567791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.569', 'subgroup_hash': 569, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1438', 'subgroup_hash': 1438, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1004', 'subgroup_hash': 1004, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1004', 'subgroup_hash': 1004, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1477', 'subgroup_hash': 1477, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.958', 'subgroup_hash': 958, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.958', 'subgroup_hash': 958, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1149', 'subgroup_hash': 1149, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1360', 'subgroup_hash': 1360, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1353', 'subgroup_hash': 1353, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.883', 'subgroup_hash': 883, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.777', 'subgroup_hash': 777, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1459', 'subgroup_hash': 1459, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1004', 'subgroup_hash': 1004, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1168', 'subgroup_hash': 1168, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1191', 'subgroup_hash': 1191, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(D_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 243567824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.668', 'subgroup_hash': 668, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.284', 'subgroup_hash': 284, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(C_8\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 243567826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1374', 'subgroup_hash': 1374, 'subgroup_order': 192, 'subgroup_tex': 'C_3:D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1477', 'subgroup_hash': 1477, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.958', 'subgroup_hash': 958, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.958', 'subgroup_hash': 958, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1477', 'subgroup_hash': 1477, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.958', 'subgroup_hash': 958, 'subgroup_order': 192, 'subgroup_tex': 'C_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1477', 'subgroup_hash': 1477, 'subgroup_order': 192, 'subgroup_tex': 'Q_8\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.973', 'subgroup_hash': 973, 'subgroup_order': 192, 'subgroup_tex': 'A_4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1015', 'subgroup_hash': 1015, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times \\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 243567839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1298', 'subgroup_hash': 1298, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.605', 'subgroup_hash': 605, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.290', 'subgroup_hash': 290, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1366', 'subgroup_hash': 1366, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243567843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 96, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.599', 'subgroup_hash': 599, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.898', 'subgroup_hash': 898, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.600', 'subgroup_hash': 600, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.881', 'subgroup_hash': 881, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1490', 'subgroup_hash': 1490, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.297', 'subgroup_hash': 297, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.607', 'subgroup_hash': 607, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.673', 'subgroup_hash': 673, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.786', 'subgroup_hash': 786, 'subgroup_order': 192, 'subgroup_tex': '(C_3\\times Q_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.980', 'subgroup_hash': 980, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.976', 'subgroup_hash': 976, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1490', 'subgroup_hash': 1490, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1490', 'subgroup_hash': 1490, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.36.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 144, 'counter': 676, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 144, 'counter': 677, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 144, 'counter': 678, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 144, 'counter': 679, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 144, 'counter': 680, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 144, 'counter': 681, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 144, 'counter': 682, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.156', 'subgroup_hash': 156, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.137', 'subgroup_hash': 137, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.69', 'subgroup_hash': 69, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243567909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.52', 'subgroup_hash': 52, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.164', 'subgroup_hash': 164, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.150', 'subgroup_hash': 150, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.150', 'subgroup_hash': 150, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.156', 'subgroup_hash': 156, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 243567943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243567953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243567969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.156', 'subgroup_hash': 156, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.137', 'subgroup_hash': 137, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.69', 'subgroup_hash': 69, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243567979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.52', 'subgroup_hash': 52, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.164', 'subgroup_hash': 164, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.81', 'subgroup_hash': 81, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.81', 'subgroup_hash': 81, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.97', 'subgroup_hash': 97, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.107', 'subgroup_hash': 107, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243567991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.128', 'subgroup_hash': 128, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243567997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.140', 'subgroup_hash': 140, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.85', 'subgroup_hash': 85, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243568000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.53', 'subgroup_hash': 53, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.174', 'subgroup_hash': 174, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.71', 'subgroup_hash': 71, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.58', 'subgroup_hash': 58, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.59', 'subgroup_hash': 59, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.82', 'subgroup_hash': 82, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.58', 'subgroup_hash': 58, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.71', 'subgroup_hash': 71, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.59', 'subgroup_hash': 59, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.82', 'subgroup_hash': 82, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.122', 'subgroup_hash': 122, 'subgroup_order': 144, 'subgroup_tex': 'C_3\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.60', 'subgroup_hash': 60, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.60', 'subgroup_hash': 60, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.87', 'subgroup_hash': 87, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243568025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.98', 'subgroup_hash': 98, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.125', 'subgroup_hash': 125, 'subgroup_order': 144, 'subgroup_tex': 'C_3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243568035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 243568046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.48.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1729', 'subgroup_hash': 1729, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2307', 'subgroup_hash': 2307, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1779', 'subgroup_hash': 1779, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1730', 'subgroup_hash': 1730, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1762', 'subgroup_hash': 1762, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1669', 'subgroup_hash': 1669, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1875', 'subgroup_hash': 1875, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1764', 'subgroup_hash': 1764, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2194', 'subgroup_hash': 2194, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\times D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1658', 'subgroup_hash': 1658, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2198', 'subgroup_hash': 2198, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1729', 'subgroup_hash': 1729, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2307', 'subgroup_hash': 2307, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1779', 'subgroup_hash': 1779, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1730', 'subgroup_hash': 1730, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.54.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2013', 'subgroup_hash': 2013, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.64.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 900, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.222', 'subgroup_hash': 222, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243568129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 96, 'counter': 901, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 902, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.199', 'subgroup_hash': 199, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 243568145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243568146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243568161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.78', 'subgroup_hash': 78, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243568178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ms1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.my1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.mz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.na1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243568218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243568227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243568229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243568231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243568234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243568235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.205', 'subgroup_hash': 205, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243568236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564564
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.176', 'subgroup_hash': 176, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.48', 'subgroup_hash': 48, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.127', 'subgroup_hash': 127, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243564567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.37', 'subgroup_hash': 37, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.222', 'subgroup_hash': 222, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243564570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.104', 'subgroup_hash': 104, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.104', 'subgroup_hash': 104, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.174', 'subgroup_hash': 174, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.147', 'subgroup_hash': 147, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.81', 'subgroup_hash': 81, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.75', 'subgroup_hash': 75, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.76', 'subgroup_hash': 76, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.46', 'subgroup_hash': 46, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.55', 'subgroup_hash': 55, 'subgroup_order': 96, 'subgroup_tex': 'C_4:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.9', 'subgroup_hash': 9, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.11', 'subgroup_hash': 11, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.175', 'subgroup_hash': 175, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 243564719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.151', 'subgroup_hash': 151, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.20', 'subgroup_hash': 20, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.21', 'subgroup_hash': 21, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.20', 'subgroup_hash': 20, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.21', 'subgroup_hash': 21, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.151', 'subgroup_hash': 151, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.56', 'subgroup_hash': 56, 'subgroup_order': 96, 'subgroup_tex': 'C_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.15', 'subgroup_hash': 15, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.53', 'subgroup_hash': 53, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.42', 'subgroup_hash': 42, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.15', 'subgroup_hash': 15, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.24', 'subgroup_hash': 24, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.53', 'subgroup_hash': 53, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.42', 'subgroup_hash': 42, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.166', 'subgroup_hash': 166, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.152', 'subgroup_hash': 152, 'subgroup_order': 96, 'subgroup_tex': 'C_3:C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.53', 'subgroup_hash': 53, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.42', 'subgroup_hash': 42, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.95', 'subgroup_hash': 95, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.95', 'subgroup_hash': 95, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243564747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.69', 'subgroup_hash': 69, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.69', 'subgroup_hash': 69, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.66', 'subgroup_hash': 66, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.66', 'subgroup_hash': 66, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.69', 'subgroup_hash': 69, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.66', 'subgroup_hash': 66, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243564755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243564775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243564778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 243564793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.205', 'subgroup_hash': 205, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243564806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.176', 'subgroup_hash': 176, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.127', 'subgroup_hash': 127, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243564811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.48', 'subgroup_hash': 48, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243564812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.37', 'subgroup_hash': 37, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243564813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.199', 'subgroup_hash': 199, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.65', 'subgroup_hash': 65, 'subgroup_order': 96, 'subgroup_tex': 'A_4:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 243564827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.199', 'subgroup_hash': 199, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.203', 'subgroup_hash': 203, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.203', 'subgroup_hash': 203, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ne1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ng1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ni1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.no1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 48, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.np1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ns1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ny1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.nz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ob1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.od1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.of1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.og1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ok1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ol1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.om1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.on1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.op1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.or1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.os1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ot1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ou1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ov1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ow1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ox1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.oz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ph1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.po1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.po1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ps1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.ps1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.px1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.px1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.pz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.py1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.py1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.pz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243564921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.72.qk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.qk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 72, 'counter': 1327, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 72, 'counter': 1328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243564928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 1329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.189', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 189, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 72, 'counter': 1330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.189', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 189, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 1331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.96.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.189', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 189, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243564948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243564963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 1361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 1362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243564968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564969
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243564980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243564988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243564989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243564990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 1385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243564991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 1388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243564999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.14', 'subgroup_hash': 14, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.13', 'subgroup_hash': 13, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.38', 'subgroup_hash': 38, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 1413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 1415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 1427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 1463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 1474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 1475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 1487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.96.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.246', 'subgroup_hash': 246, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.87', 'subgroup_hash': 87, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.262', 'subgroup_hash': 262, 'subgroup_order': 64, 'subgroup_tex': 'Q_8\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.83', 'subgroup_hash': 83, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.103', 'subgroup_hash': 103, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.212', 'subgroup_hash': 212, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.106', 'subgroup_hash': 106, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.96', 'subgroup_hash': 96, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.96', 'subgroup_hash': 96, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.197', 'subgroup_hash': 197, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.96', 'subgroup_hash': 96, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.246', 'subgroup_hash': 246, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.87', 'subgroup_hash': 87, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.262', 'subgroup_hash': 262, 'subgroup_order': 64, 'subgroup_tex': 'Q_8\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 1637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 1639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 32, 'counter': 1645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.230', 'subgroup_hash': 230, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 1654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 1658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 1662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.108.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 1667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 1668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.128.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 48, 'counter': 1675, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 1676, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 288, 'characteristic': True, 'core_order': 48, 'counter': 1677, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 288, 'characteristic': True, 'core_order': 48, 'counter': 1678, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565336
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 12, 'counter': 1702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 1706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 12, 'counter': 1707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 1718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 1724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 12, 'counter': 1726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 1727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 1730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 1731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 1835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 1837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 1855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 1858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 24, 'counter': 1861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 1862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 1863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565522
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 1871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 1887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 1888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243565549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243565582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 1920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 1922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 1923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 1930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 1931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 1946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 1947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 1960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 24, 'counter': 1966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 1970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 1971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 1972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 1973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 1988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 1995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 2003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 2004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ms1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 2006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 2010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.mz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.my1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.na1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 2016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 2017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ne1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ng1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ni1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 2026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.no1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 2028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.np1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 2029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ns1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 2033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 2034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.nx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ny1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ob1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.od1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 2043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.of1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.og1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 2046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ok1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ol1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.om1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.on1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.op1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 2055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.or1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.os1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 2058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ot1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ou1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ov1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ow1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 2062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ox1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.oz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 2065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 2066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 2068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243565752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.px1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.py1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 2077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.pm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 2078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.po1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 2080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ps1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.px1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.py1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.pz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ql1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 2092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 2093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 2094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243565780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ph1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.po1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.qg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ps1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ql1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.pw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 2114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.qx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 2115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.qz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.qz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ra1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ra1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 2119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 2120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.re1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.re1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.ri1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ri1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.144.rk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.rk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 36, 'counter': 2128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1475', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1475, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 2129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 2130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 2131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 2132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 2134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 2136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 2137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565828
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 2139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 2141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 2142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 2145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 2148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 2150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 2153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 2154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 2159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 2164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 2175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 2179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 2180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243565889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 2195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 2196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 2197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 2198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 2199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 2200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243565898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243565924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.192.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 32, 'counter': 2233, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 243565935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243565952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 2253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 2261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 243565966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 2264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243565977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 2275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243565991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243565997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243565999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 2302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 2351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 2421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566144
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566152
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 2455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 2459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243566192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 2469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 2472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 2474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 2475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 2476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 2478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566211
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 2493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 2509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 2535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 2537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.216.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2538, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '6912.ia.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 243566272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 24, 'counter': 2539, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 24, 'counter': 2540, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 24, 'counter': 2541, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.288.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 24, 'counter': 2542, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.288.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '288.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 24, 'counter': 2543, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.288.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '288.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.851', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 851, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 288, 'characteristic': False, 'core_order': 24, 'counter': 2544, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.288.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '288.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.851', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 851, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566280
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566282
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 12, 'counter': 2556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 12, 'counter': 2557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 2558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 2559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 2560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 12, 'counter': 2561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 2562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 2563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566300
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 2564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 2565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 2566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566308
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566310
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566325
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 2587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 2588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 2598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 2602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 2604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 2605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 2606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 2607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 2608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566364
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566366
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 2637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 2638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 2654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 2655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 2700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566456
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 2704, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566457
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2705, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566458
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566459
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2707, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566460
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 2708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566461
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566468
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 2715, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566469
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 2717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 2718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566476
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 2722, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566477
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2723, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566478
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566479
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 2726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 2727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 2728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 2729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566485
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 2730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 243566486
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 2732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 2733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 2734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 2735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 2736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 243566492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566494
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 2744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 2745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 2746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566505
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566516
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 2761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 2765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 2767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 2768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 12, 'counter': 2831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 2832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 2833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 2834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 2835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 2836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 2837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 2838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 2839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 2840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 2841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 2843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 2844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 2846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 2847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 2848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 2849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 2851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 2852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ms1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 2855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 2856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 243566625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243566644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.my1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.mz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.288.na1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 2878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 2879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 2880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 2881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 2882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 2883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 2884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 2887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 2888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243566669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.384.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '384.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243566697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 2921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 2925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 2926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 8, 'counter': 2931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 2946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 2947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 2949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 2953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 2958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 2963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566747
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 2981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 2986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 2988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 2995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 2996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 2997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 2999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566824
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 3039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 243566834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 8, 'counter': 3054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 3055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 3056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 3057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 3058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 3059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 3060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 3061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 3062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 3063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 3085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 3105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 8, 'counter': 3118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 3132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243566934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 3141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 3149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 3157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 3167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 3177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 243566985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566990
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 3187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 3188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 3189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 243566997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243566999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 3200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 3201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 3202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 3203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.432.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 12, 'counter': 3204, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '576.8653', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8653, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 12, 'counter': 3205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.576.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '576.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '576.8325', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8325, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 12, 'counter': 3206, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.576.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '576.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '576.8325', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8325, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 3209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 6, 'counter': 3210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567021
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 3212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 3213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 3214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 3215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 6, 'counter': 3218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 6, 'counter': 3219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 3220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567031
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 3221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 3224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 3227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 3230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 3233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 3235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 3236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 3237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 3240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 3244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 3245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 3246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567059
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 3247, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567060
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 3248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567061
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 3249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567063
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 3250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567064
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 3251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567065
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 3252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567066
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 3253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567067
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3254, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567068
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567069
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567070
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 3257, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567071
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 3258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 6, 'counter': 3269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 6, 'counter': 3270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 3271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 3272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 3273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 3274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567096
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567109
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567119
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567120
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567122
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567123
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3304, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567124
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567125
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567126
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567127
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3308, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567128
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 3310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 3311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 3312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 3313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 3314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 243567135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567141
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567143
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567145
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567150
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3337, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.576.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 243567160
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567164
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567166
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.576.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567198
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 3372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567199
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 3373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 3374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567204
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.768.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567205
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 8, 'counter': 3379, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.864.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '864.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '864.4673', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4673, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 8, 'counter': 3380, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.864.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '864.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '864.4673', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4673, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 2, 'counter': 3381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567211
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 2, 'counter': 3389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567218
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567225
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567226
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 2, 'counter': 3399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567239
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567245
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567246
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567248
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567249
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567250
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567252
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567254
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567256
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 3433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567274
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567303
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 2, 'counter': 3467, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567304
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3468, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567305
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3469, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567307
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3470, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567308
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3471, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567309
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3472, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3478, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3479, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 3480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 3481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 243567320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567325
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567327
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 4, 'counter': 3489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567364
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567365
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 4, 'counter': 3525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 3526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 3527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 3528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 3529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 3530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.864.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 243567388
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 3456, 'characteristic': True, 'core_order': 6, 'counter': 3543, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '6912.ia.1152.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1152.157851', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5440091439875999871, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567389
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 6, 'counter': 3544, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6912.ia.1152.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1152.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1152.157461', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7371672288863537087, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 2, 'counter': 3545, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 2, 'counter': 3546, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567392
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 3547, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567393
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 3548, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567394
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 3549, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 3550, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3551, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567398
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3552, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567399
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3553, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567400
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 3, 'counter': 3554, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567401
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3555, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3556, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567403
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 3, 'counter': 3557, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3558, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567405
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3559, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567407
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 3560, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567408
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3561, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567409
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3562, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567410
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567411
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3564, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567412
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 3, 'counter': 3565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567413
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 3566, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567414
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3567, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567415
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3568, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567416
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567418
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3570, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567419
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 3571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567420
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567421
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3574, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567423
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567424
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3576, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567425
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 3577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567426
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567427
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567429
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 3580, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 243567430
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567431
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567432
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567433
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 3584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567434
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567435
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567436
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 3587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567437
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567438
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567440
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567441
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567442
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567443
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1152.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1152.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 4, 'counter': 3594, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6912.ia.1728.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1728.46336', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46336, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2\\times \\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': False, 'core_order': 2, 'counter': 3595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': False, 'core_order': 2, 'counter': 3596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 2, 'counter': 3597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 2, 'counter': 3598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 2, 'counter': 3599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 3603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 3605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567458
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 2, 'counter': 3606, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567459
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3607, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567460
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 3608, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567461
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 3609, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 3610, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567464
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 3611, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 1, 'counter': 3612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 1, 'counter': 3613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567482
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3628, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567483
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3629, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567485
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3630, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567486
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3631, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567497
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3641, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567498
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3642, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 243567499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6912.ia.1728.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 243567513
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 3456, 'characteristic': True, 'core_order': 3, 'counter': 3656, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '6912.ia.2304.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2304.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2304.d', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8112084019139883741, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2304, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2.S_4^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3657, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567515
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3658, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567516
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3659, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3660, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567519
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3661, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567520
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3662, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.2304.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2304.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2304, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 243567521
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 6912, 'characteristic': True, 'core_order': 2, 'counter': 3663, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '6912.ia.3456.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '3456.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3456.jo', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2520327345672601111, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3456, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'D3', 'C8'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': False, 'core_order': 1, 'counter': 3664, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567523
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': False, 'core_order': 1, 'counter': 3665, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567524
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 2304, 'characteristic': False, 'core_order': 1, 'counter': 3666, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567525
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 3667, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567526
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 1, 'counter': 3668, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3669, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 3670, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3671, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3672, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3673, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3674, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3675, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6912.ia.3456.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3456.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 243567535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6912.ia', 'ambient_counter': 209, 'ambient_order': 6912, 'ambient_tex': 'D_6.S_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 6912, 'characteristic': True, 'core_order': 1, 'counter': 3676, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '6912.ia.6912.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6912.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '6912.ia', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4930085545709402789, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 6912, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6.S_4^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C9'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 243564578
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gr1', '36.bp1', '36.cw1'], 'contains': ['144.bp1', '144.bs1', '144.bw1', '144.ca1', '144.cg1', '144.dt1', '144.ed1', '216.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.72.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564579
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gr1', '36.bo1', '36.cx1'], 'contains': ['144.bp1', '144.bt1', '144.bx1', '144.cc1', '144.cf1', '144.ea1', '144.ee1', '216.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 87218570880, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.72.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564571
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.d1', '36.bn1', '36.bz1', '36.ce1', '36.cj1', '36.cp1', '36.he1'], 'contains': ['144.fr1', '144.jn1', '216.bx1', '288.j1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564572
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.ck1', '36.cq1', '36.hf1'], 'contains': ['144.fs1', '144.jo1', '216.bx1', '288.k1'], 'core': '864.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 32929, 36933, 93405314676, 87124129, 87109068], 'label': '6912.ia.72.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.y1', 'old_label': '72.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564573
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1', '24.n1', '36.gd1'], 'contains': ['144.bk1', '144.bl1', '144.bo1', '144.cj1', '144.ck1', '144.co1', '144.eb1', '144.qt1', '216.bz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 43909226, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.72.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564574
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1'], 'contains': ['24.bf1', '24.bi1', '24.bl1', '24.bx1', '24.by1', '24.ci1', '24.cj1', '36.gg1', '36.gr1', '48.cw1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '12.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564765
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '36.gf1', '36.hg1', '36.hj1'], 'contains': ['144.b1', '144.hb1', '144.hd1', '216.hv1', '288.dl1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 87218603809, 47537280, 36933, 40279680], 'label': '6912.ia.72.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.kw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jp1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564575
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1', '24.o1', '36.gd1'], 'contains': ['144.bl1', '144.bm1', '144.bn1', '144.cm1', '144.cn1', '144.df1', '144.dn1', '144.qu1', '216.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 43908480, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.72.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564576
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '36.gj1', '36.bn1', '36.cr1', '36.cs1', '36.ct1', '36.cu1', '36.cv1'], 'contains': ['144.fr1', '144.jw1', '216.cu1', '288.l1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.72.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565092
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '48.cb1', '48.gb1', '48.gi1', '48.gu1'], 'contains': ['192.cr1', '192.cw1', '192.cy1', '288.mm1', '288.mn1'], 'core': '576.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 43944719, 2676, 40279680], 'label': '6912.ia.96.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ga1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564577
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.gp1', '36.cw1', '36.cx1'], 'contains': ['144.bp1', '144.bq1', '144.bt1', '144.by1', '144.cd1', '144.cr1', '144.dz1', '144.qv1', '216.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 43909226, 93405312000, 43908480, 36933, 87091200], 'label': '6912.ia.72.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565093
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1', '48.cc1', '48.gc1', '48.gk1', '48.gv1'], 'contains': ['192.a1', '288.mm1', '288.mo1', '384.bg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 47537280, 40279680], 'label': '6912.ia.96.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '96.fv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564561
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['6912.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '3.a1', '3.b1', '3.c1', '4.h1', '4.i1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 40312609, 87178291200, 36933, 43909226, 47537280, 40279680, 127370880, 87109068, 93405312000, 7620480], 'label': '6912.ia.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243564562
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.d1', '6.e1', '6.f1', '6.g1', '6.o1', '6.t1', '6.h1', '6.i1', '6.j1', '6.k1', '6.x1', '6.y1', '6.bh1', '6.bl1', '9.a1', '9.c1', '12.bn1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564563
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.p1', '6.q1'], 'contains': ['24.a1', '24.bk1', '24.bl1', '24.bt1', '24.bu1', '24.cg1', '24.ch1', '36.gf1', '36.gq1', '48.cv1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564564
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.br1', '36.by1', '36.cc1', '36.cf1', '36.cm1', '36.hb1'], 'contains': ['144.bg1', '144.et1', '144.ew1', '144.jh1', '144.ji1', '216.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.72.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243564565
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.bs1', '36.bx1', '36.cd1', '36.cg1', '36.cl1', '36.hb1'], 'contains': ['144.bg1', '144.eu1', '144.ex1', '216.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.72.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243564566
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.bs1', '36.bv1', '36.cb1', '36.ci1', '36.cn1', '36.hc1'], 'contains': ['144.bg1', '144.ev1', '144.ez1', '144.jj1', '144.jk1', '216.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 87261772748], 'label': '6912.ia.72.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564567
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.br1', '36.bw1', '36.ca1', '36.ch1', '36.co1', '36.hc1'], 'contains': ['144.bg1', '144.ey1', '144.fa1', '216.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 87298060748], 'label': '6912.ia.72.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564568
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.bt1', '36.bx1', '36.cc1', '36.ch1', '36.cn1', '36.hd1'], 'contains': ['144.bg1', '144.bh1', '144.en1', '144.fb1', '144.fi1', '216.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 40297548, 36933], 'label': '6912.ia.72.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564569
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.p1', '36.bu1', '36.by1', '36.cd1', '36.ci1', '36.co1', '36.hd1'], 'contains': ['144.bg1', '144.em1', '144.fc1', '144.je1', '144.jl1', '216.bx1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.72.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564570
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.bt1', '36.ha1'], 'contains': ['144.bi1', '144.bh1', '144.bj1', '144.fg1', '144.fm1', '144.fj1', '144.fq1', '216.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127388748, 87218603809, 93405312000, 40297548, 36933], 'label': '6912.ia.72.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564580
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gs1', '36.bo1', '36.cw1'], 'contains': ['144.bp1', '144.br1', '144.bv1', '144.bz1', '144.ch1', '144.cz1', '144.dq1', '144.jx1', '144.jy1', '144.kc1', '144.kf1', '216.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87218607813, 93405312000, 40280426, 36933, 87100665], 'label': '6912.ia.72.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564581
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gs1', '36.bp1', '36.cx1', '36.da1', '36.cz1', '36.cy1', '36.db1'], 'contains': ['144.bp1', '144.bu1', '144.cb1', '144.ci1', '144.ef1', '144.jy1', '144.ka1', '144.ke1', '216.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 36933, 87305699013, 40279680], 'label': '6912.ia.72.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564582
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '36.gp1', '36.cw1', '36.dc1'], 'contains': ['144.bq1', '144.br1', '144.bs1', '144.cp1', '144.cq1', '144.cx1', '144.dj1', '144.qw1', '216.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 93405312000, 43908480, 36933, 87091200, 83468087], 'label': '6912.ia.72.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564583
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gq1', '36.cx1', '36.dc1', '36.df1', '36.dd1', '36.de1', '36.dg1'], 'contains': ['144.bq1', '144.bu1', '144.bx1', '144.cs1', '144.cv1', '144.ej1', '144.ff1', '216.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305662080, 93405312000, 32929, 36933, 119750400, 87124129], 'label': '6912.ia.72.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564584
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gq1', '36.cw1', '36.df1'], 'contains': ['144.bq1', '144.bv1', '144.bw1', '144.cu1', '144.ct1', '144.fe1', '144.fd1', '216.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87305662080, 93405312000, 40297548, 36933, 119750400], 'label': '6912.ia.72.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564585
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.r1', '6.s1'], 'contains': ['24.bf1', '24.bk1', '24.bw1', '24.bz1', '24.ck1', '36.gh1', '36.gs1', '48.cx1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564586
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gr1', '36.bo1', '36.dc1'], 'contains': ['144.br1', '144.bs1', '144.bx1', '144.cy1', '144.dd1', '144.dh1', '144.dl1', '216.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 87218570880, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.72.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564587
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gr1', '36.bq1', '36.cw1'], 'contains': ['144.br1', '144.bt1', '144.bw1', '144.db1', '144.dc1', '144.di1', '144.dm1', '216.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 43909226, 93405312000, 36933, 83471865, 87091200], 'label': '6912.ia.72.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564588
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gs1', '36.bq1', '36.dc1', '36.dj1', '36.di1', '36.dh1', '36.dk1'], 'contains': ['144.br1', '144.bu1', '144.cw1', '144.de1', '144.dr1', '144.kc1', '144.kd1', '144.ke1', '216.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87127439, 87305699013, 40279680], 'label': '6912.ia.72.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564589
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gt1', '36.bo1', '36.cw1'], 'contains': ['144.bs1', '144.bt1', '144.bv1', '144.du1', '144.dv1', '144.eg1', '144.fn1', '216.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 87305662080, 93405312000, 36933, 87091200], 'label': '6912.ia.72.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564590
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gt1', '36.bp1', '36.dc1', '36.dn1', '36.dm1', '36.dl1', '36.do1'], 'contains': ['144.bs1', '144.bu1', '144.dw1', '144.dx1', '144.es1', '216.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 93405312000, 36933, 87100665], 'label': '6912.ia.72.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564591
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gt1', '36.bq1', '36.cx1', '36.dr1', '36.dq1', '36.dp1', '36.ds1'], 'contains': ['144.bt1', '144.bu1', '144.eh1', '144.ei1', '144.ep1', '216.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.72.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564592
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.bt1', '36.da1', '36.df1', '36.dj1', '36.dn1', '36.dr1'], 'contains': ['144.bu1', '144.bv1', '144.ek1', '144.fb1', '144.fg1', '144.ki1', '144.kj1', '144.ks1', '216.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 127370880, 87218570880, 40312609, 93405312000, 36933], 'label': '6912.ia.72.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564593
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gu1', '36.bt1', '36.cz1', '36.dg1', '36.di1', '36.dm1', '36.dq1'], 'contains': ['144.bu1', '144.bx1', '144.en1', '144.eq1', '144.fq1', '216.co1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305662080, 93405312000, 32929, 43926348, 36933, 87124129], 'label': '6912.ia.72.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564594
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gu1', '36.bu1', '36.cy1', '36.df1', '36.dh1', '36.dl1', '36.dp1'], 'contains': ['144.bu1', '144.bw1', '144.em1', '144.er1', '144.fp1', '216.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305662080, 93405312000, 32929, 36933, 87124129, 83480268], 'label': '6912.ia.72.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564595
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gv1', '36.br1', '36.db1', '36.dd1', '36.dj1', '36.dl1', '36.dq1'], 'contains': ['144.bu1', '144.et1', '144.ey1', '144.kl1', '144.kn1', '216.cp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 19148, 36933, 87305699013, 40279680], 'label': '6912.ia.72.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564596
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.u1', '6.v1'], 'contains': ['24.bi1', '24.bk1', '24.cl1', '24.cm1', '24.cn1', '36.gi1', '36.gt1', '48.cy1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564597
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gv1', '36.bs1', '36.da1', '36.de1', '36.dk1', '36.dm1', '36.dp1'], 'contains': ['144.bu1', '144.eu1', '144.ev1', '144.km1', '144.kn1', '216.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 93405312000, 36933, 87305699013, 40279680], 'label': '6912.ia.72.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564598
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gw1', '36.br1', '36.cy1', '36.de1', '36.di1', '36.do1', '36.dr1'], 'contains': ['144.bu1', '144.ew1', '144.fa1', '216.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.72.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564599
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gw1', '36.bs1', '36.cz1', '36.dd1', '36.dh1', '36.dn1', '36.ds1'], 'contains': ['144.bu1', '144.ex1', '144.ez1', '216.cs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.72.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564600
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '36.a1', '36.bu1', '36.db1', '36.dg1', '36.dk1', '36.do1', '36.ds1'], 'contains': ['144.bu1', '144.eo1', '144.fc1', '144.kj1', '144.kp1', '216.cu1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.72.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564601
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gu1', '36.bt1', '36.df1'], 'contains': ['144.bv1', '144.bx1', '144.bw1', '144.fm1', '144.fl1', '144.fi1', '144.fj1', '216.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87305662080, 93405312000, 40297548, 36933, 83495329], 'label': '6912.ia.72.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564602
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.cw1', '36.hn1'], 'contains': ['144.by1', '144.bz1', '144.ca1', '144.cq1', '144.cu1', '144.di1', '144.du1', '144.kv1', '144.kw1', '144.ln1', '144.lo1', '216.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87265391865, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.72.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564603
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.cx1', '36.hn1'], 'contains': ['144.by1', '144.cb1', '144.cf1', '144.cr1', '144.cv1', '144.ea1', '144.eh1', '216.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 43909226, 93405312000, 36933, 87091200, 87305671545], 'label': '6912.ia.72.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564604
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.cw1', '36.ho1'], 'contains': ['144.by1', '144.cg1', '144.ch1', '144.cp1', '144.ct1', '144.db1', '144.eg1', '216.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 87185911680, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.72.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564605
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.cw1', '36.gx1'], 'contains': ['144.bz1', '144.cd1', '144.cg1', '144.dj1', '144.dm1', '144.fe1', '144.fn1', '216.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 87265391865, 36933, 87091200], 'label': '6912.ia.72.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564606
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.bo1', '36.hn1'], 'contains': ['144.bz1', '144.ce1', '144.cf1', '144.dk1', '144.dl1', '144.fk1', '144.fn1', '216.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 43909226, 93405312000, 87265391865, 36933, 87091200], 'label': '6912.ia.72.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564607
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.r1', '6.u1'], 'contains': ['24.bk1', '24.bl1', '24.cp1', '24.cq1', '24.cv1', '36.gk1', '36.gu1', '48.cz1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.12.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564608
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.bp1', '36.hn1'], 'contains': ['144.ca1', '144.cb1', '144.ce1', '144.ds1', '144.dw1', '144.ed1', '144.fo1', '216.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83471865, 87091200, 83468087, 87305671545], 'label': '6912.ia.72.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564609
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.cx1', '36.gx1'], 'contains': ['144.cb1', '144.cc1', '144.cd1', '144.dz1', '144.ee1', '144.eh1', '144.ff1', '216.dc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 36933, 87091200, 87305671545], 'label': '6912.ia.72.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564610
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.cw1', '36.gy1'], 'contains': ['144.ca1', '144.cd1', '144.ch1', '144.cx1', '144.dc1', '144.dv1', '144.fd1', '216.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 93405312000, 36933, 119750400, 87091200], 'label': '6912.ia.72.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243564611
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.bo1', '36.ho1'], 'contains': ['144.cc1', '144.ce1', '144.ch1', '144.da1', '144.dd1', '144.eg1', '144.fh1', '216.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 93405312000, 87222200426, 36933, 87091200, 87298041600], 'label': '6912.ia.72.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564612
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.cx1', '36.dt1', '36.du1', '36.dv1', '36.dw1', '36.ho1'], 'contains': ['144.by1', '144.cc1', '144.ci1', '144.cs1', '144.ei1', '144.kt1', '144.kx1', '144.lp1', '216.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 87185911680, 93405312000, 36933, 87100665], 'label': '6912.ia.72.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564613
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.cx1', '36.dx1', '36.dy1', '36.dz1', '36.ed1', '36.gy1'], 'contains': ['144.cd1', '144.cf1', '144.ci1', '144.ej1', '144.ep1', '216.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 43945413, 36933, 87100665], 'label': '6912.ia.72.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564614
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.bv1', '36.da1', '36.dt1', '36.dx1', '36.ea1', '36.hr1'], 'contains': ['144.ci1', '144.ek1', '144.ev1', '144.lb1', '144.ld1', '144.ml1', '144.mn1', '216.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 87218588748, 36933, 40279680], 'label': '6912.ia.72.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564615
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.bp1', '36.ea1', '36.eb1', '36.ec1', '36.ee1', '36.ho1'], 'contains': ['144.ce1', '144.cg1', '144.ci1', '144.el1', '144.es1', '216.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222200426, 87222236613, 36933, 87100665], 'label': '6912.ia.72.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565094
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '48.cd1', '48.gd1'], 'contains': ['192.cz1', '288.mm1', '288.mp1', '384.bh1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 43944719, 40279680], 'label': '6912.ia.96.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '96.fw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564616
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.bx1', '36.cz1', '36.du1', '36.ea1', '36.ed1', '36.hs1'], 'contains': ['144.ci1', '144.en1', '144.ex1', '216.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.72.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564617
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.by1', '36.cy1', '36.dt1', '36.dz1', '36.eb1', '36.hs1'], 'contains': ['144.ci1', '144.em1', '144.ew1', '144.lc1', '144.mm1', '216.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.72.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564618
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.s1', '6.u1'], 'contains': ['24.bk1', '24.cr1', '24.cs1', '36.gl1', '36.gv1', '48.da1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564619
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.bw1', '36.db1', '36.du1', '36.dy1', '36.eb1', '36.hr1'], 'contains': ['144.ci1', '144.eo1', '144.ey1', '144.ld1', '144.mo1', '216.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 36933, 87265400268, 40279680], 'label': '6912.ia.72.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564620
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.bv1', '36.cz1', '36.dw1', '36.dy1', '36.ec1', '36.ht1'], 'contains': ['144.ci1', '144.eq1', '144.ez1', '144.le1', '144.mp1', '216.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87261771468, 87261772748], 'label': '6912.ia.72.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564621
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.bw1', '36.cy1', '36.dv1', '36.dx1', '36.ee1', '36.ht1'], 'contains': ['144.ci1', '144.er1', '144.fa1', '216.dn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 93405312000, 36933, 87100665, 87298060748], 'label': '6912.ia.72.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564622
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.bx1', '36.da1', '36.dv1', '36.dz1', '36.ec1', '36.hu1'], 'contains': ['144.ci1', '144.eu1', '144.fb1', '144.la1', '144.mk1', '216.do1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 36933, 746], 'label': '6912.ia.72.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564623
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '36.v1', '36.by1', '36.db1', '36.dw1', '36.ed1', '36.ee1', '36.hu1'], 'contains': ['144.ci1', '144.et1', '144.fc1', '144.la1', '144.lf1', '144.mj1', '144.mq1', '216.dp1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 40297548, 36933, 40279680], 'label': '6912.ia.72.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243564624
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '36.c1', '36.e1', '36.bz1', '36.cr1', '36.ef1', '36.eg1', '36.eh1'], 'contains': ['144.d1', '144.fr1', '144.mt1', '216.dp1', '288.o1'], 'core': '144.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 40280426, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.72.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564625
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '36.d1', '36.cs1', '36.ef1', '36.ei1', '36.ej1', '36.ek1', '36.ib1'], 'contains': ['144.fr1', '144.lm1', '216.ed1', '288.p1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564626
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.dc1', '36.hn1'], 'contains': ['144.cp1', '144.cq1', '144.cv1', '144.cw1', '144.cy1', '144.dl1', '144.dw1', '216.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.72.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564627
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.cw1', '36.hn1'], 'contains': ['144.cp1', '144.cr1', '144.cu1', '144.cz1', '144.dc1', '144.ed1', '144.fn1', '216.dr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 87265391865, 36933, 83471865, 87091200], 'label': '6912.ia.72.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564628
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.dc1', '36.el1', '36.em1', '36.en1', '36.eo1', '36.ho1'], 'contains': ['144.cp1', '144.cs1', '144.dd1', '144.de1', '144.es1', '216.ds1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 87222200426, 36933, 87100665], 'label': '6912.ia.72.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564629
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.r1', '6.v1'], 'contains': ['24.bk1', '24.ct1', '24.cu1', '36.gm1', '36.gw1', '48.db1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87178291200, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.12.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564630
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.cw1', '36.id1'], 'contains': ['144.cq1', '144.cr1', '144.ct1', '144.dm1', '144.dq1', '144.dt1', '144.dv1', '216.dt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 87185911680, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.72.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564631
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.dc1', '36.ep1', '36.eq1', '36.er1', '36.es1', '36.id1'], 'contains': ['144.cq1', '144.cs1', '144.dh1', '144.dr1', '144.dx1', '144.lr1', '144.ls1', '144.lt1', '216.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 87185911680, 93405312000, 36933, 87100665], 'label': '6912.ia.72.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564632
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.cx1', '36.et1', '36.eu1', '36.ev1', '36.ew1', '36.id1'], 'contains': ['144.cr1', '144.cs1', '144.ee1', '144.ef1', '144.ep1', '216.dv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.72.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564633
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.df1', '36.dt1', '36.el1', '36.ep1', '36.et1', '36.ie1'], 'contains': ['144.cs1', '144.cu1', '144.ek1', '144.em1', '144.fl1', '144.lv1', '144.lw1', '144.mc1', '216.dw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87265400268, 87124129, 83480268], 'label': '6912.ia.72.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243566343
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ip1', '96.p1', '144.dp1', '144.ec1', '144.fy1'], 'contains': ['576.f1', '576.ey1', '864.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [43908480, 36933, 93405314676, 87091200], 'label': '6912.ia.288.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '288.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243564634
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.dg1', '36.du1', '36.em1', '36.eq1', '36.eu1', '36.ie1'], 'contains': ['144.cs1', '144.cv1', '144.en1', '144.eo1', '144.fq1', '216.dx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43926348, 87218588748, 36933, 87124129], 'label': '6912.ia.72.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564635
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.dd1', '36.dw1', '36.en1', '36.ep1', '36.eu1', '36.if1'], 'contains': ['144.cs1', '144.et1', '144.ez1', '144.lx1', '144.ly1', '216.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87100665, 87261772748], 'label': '6912.ia.72.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564636
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.de1', '36.dv1', '36.eo1', '36.eq1', '36.et1', '36.if1'], 'contains': ['144.cs1', '144.eu1', '144.fa1', '216.dz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87100665, 87298060748], 'label': '6912.ia.72.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564637
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.de1', '36.dt1', '36.em1', '36.es1', '36.ev1', '36.ig1'], 'contains': ['144.cs1', '144.ev1', '144.ew1', '144.lz1', '144.ma1', '216.ea1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.72.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564638
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.dd1', '36.du1', '36.el1', '36.er1', '36.ew1', '36.ig1'], 'contains': ['144.cs1', '144.ex1', '144.ey1', '216.eb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.72.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564639
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.df1', '36.dv1', '36.en1', '36.er1', '36.ev1', '36.ih1'], 'contains': ['144.cs1', '144.ct1', '144.er1', '144.fb1', '144.fj1', '216.ec1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 93405312000, 40297548, 36933], 'label': '6912.ia.72.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564640
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.w1'], 'contains': ['24.cw1', '36.a1', '36.go1', '48.bm1', '48.dd1', '48.de1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.12.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '12.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1', 'subgroup_fusion': None, 'weyl_group': '1728.47859'}
  • id: 243564641
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '36.p1', '36.dg1', '36.dw1', '36.eo1', '36.es1', '36.ew1', '36.ih1'], 'contains': ['144.cs1', '144.eq1', '144.fc1', '144.lu1', '144.mb1', '216.ed1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.72.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564642
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.df1', '36.ie1'], 'contains': ['144.cu1', '144.ct1', '144.cv1', '144.fg1', '144.fm1', '144.fi1', '144.fp1', '216.ee1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 127388748, 87218603809, 93405312000, 40297548, 36933], 'label': '6912.ia.72.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564643
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.dc1', '36.gx1'], 'contains': ['144.cw1', '144.cx1', '144.dd1', '144.dh1', '144.dj1', '144.dw1', '144.ff1', '216.ef1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.72.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564644
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.bq1', '36.hn1'], 'contains': ['144.cw1', '144.da1', '144.dc1', '144.di1', '144.dk1', '144.eh1', '144.fo1', '216.eg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 83471865, 87091200, 87305671545], 'label': '6912.ia.72.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564645
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.cw1', '36.gx1'], 'contains': ['144.cx1', '144.cz1', '144.db1', '144.dt1', '144.du1', '144.dz1', '144.fe1', '216.eh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.72.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564646
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.bo1', '36.hn1'], 'contains': ['144.cy1', '144.cz1', '144.da1', '144.ds1', '144.du1', '144.ea1', '144.fk1', '216.ei1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.72.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564647
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.dc1', '36.ex1', '36.ey1', '36.ez1', '36.fa1', '36.gy1'], 'contains': ['144.cx1', '144.cy1', '144.de1', '144.dx1', '144.ej1', '216.ej1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 43945413, 36933, 87100665], 'label': '6912.ia.72.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564648
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.bq1', '36.fb1', '36.fc1', '36.fd1', '36.fe1', '36.ho1'], 'contains': ['144.da1', '144.db1', '144.de1', '144.ei1', '144.el1', '216.ek1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 93405312000, 87222236613, 36933, 87100665], 'label': '6912.ia.72.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564649
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '36.ca1', '36.dj1', '36.el1', '36.ex1', '36.fb1', '36.hr1'], 'contains': ['144.de1', '144.ek1', '144.ey1', '144.ml1', '144.mo1', '216.el1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87218588748, 36933, 87127439, 40279680], 'label': '6912.ia.72.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564650
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.cc1', '36.di1', '36.em1', '36.fa1', '36.fb1', '36.hs1'], 'contains': ['144.de1', '144.en1', '144.ew1', '216.en1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.72.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564651
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '6.d1'], 'contains': ['24.e1', '24.dd1', '24.dk1', '24.dq1', '24.ds1', '24.eh1', '24.em1', '36.jw1', '36.ka1', '48.cs1'], 'core': '24.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87178291200, 36933, 2676, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.12.dq1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564652
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '36.cd1', '36.dh1', '36.el1', '36.ez1', '36.fc1', '36.hs1'], 'contains': ['144.de1', '144.em1', '144.ex1', '144.mr1', '216.em1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.72.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564653
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.cb1', '36.dk1', '36.em1', '36.ey1', '36.fc1', '36.hr1'], 'contains': ['144.de1', '144.eo1', '144.ev1', '144.mn1', '144.mo1', '216.eo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87127439, 87265400268, 40279680], 'label': '6912.ia.72.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564654
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '36.ca1', '36.di1', '36.eo1', '36.ey1', '36.fd1', '36.ht1'], 'contains': ['144.de1', '144.eq1', '144.fa1', '144.ms1', '216.ep1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87298060748, 87261771468], 'label': '6912.ia.72.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564655
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.cb1', '36.dh1', '36.en1', '36.ex1', '36.fe1', '36.ht1'], 'contains': ['144.de1', '144.er1', '144.ez1', '216.eq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 93405312000, 36933, 87100665, 87261772748], 'label': '6912.ia.72.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564656
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.cc1', '36.dj1', '36.en1', '36.ez1', '36.fd1', '36.hu1'], 'contains': ['144.de1', '144.et1', '144.fb1', '144.mj1', '144.mk1', '216.er1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40280426, 40297548, 36933], 'label': '6912.ia.72.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564657
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '36.ba1', '36.cd1', '36.dk1', '36.eo1', '36.fa1', '36.fe1', '36.hu1'], 'contains': ['144.de1', '144.eu1', '144.fc1', '144.mk1', '144.mq1', '216.es1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 40297548, 36933, 40279680], 'label': '6912.ia.72.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fi1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564658
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '36.c1', '36.f1', '36.ce1', '36.ct1', '36.ei1', '36.ff1', '36.fg1'], 'contains': ['144.fr1', '144.mt1', '216.es1', '288.s1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 127390028, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.72.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564659
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.bo1', '36.id1'], 'contains': ['144.dh1', '144.dk1', '144.dq1', '144.ds1', '144.dv1', '144.ee1', '144.fh1', '216.et1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 93405312000, 36933, 87091200, 87298041600], 'label': '6912.ia.72.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fk1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564660
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.cw1', '36.gz1'], 'contains': ['144.di1', '144.dj1', '144.dq1', '144.dz1', '144.ed1', '144.eg1', '144.fd1', '216.eu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 93405312000, 87222200426, 36933, 119750400, 87091200], 'label': '6912.ia.72.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fl1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564661
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.dc1', '36.fh1', '36.fi1', '36.fj1', '36.fn1', '36.gz1'], 'contains': ['144.dj1', '144.dl1', '144.dr1', '144.ej1', '144.es1', '216.ev1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 87222200426, 36933, 87100665], 'label': '6912.ia.72.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564662
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1'], 'contains': ['24.dd1', '24.dj1', '24.dk1', '24.dr1', '24.dt1', '24.ek1', '24.en1', '36.jx1', '36.kc1', '48.ct1'], 'core': '48.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 87178291200, 36933, 2676, 83463146], 'label': '6912.ia.12.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564663
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.cf1', '36.dj1', '36.ep1', '36.fh1', '36.fk1', '36.is1'], 'contains': ['144.dr1', '144.ek1', '144.et1', '144.mz1', '144.nb1', '144.nz1', '144.ob1', '216.ew1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87218588748, 19148, 36933, 40279680], 'label': '6912.ia.72.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fn1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564664
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.bq1', '36.fk1', '36.fl1', '36.fm1', '36.fo1', '36.id1'], 'contains': ['144.dk1', '144.dm1', '144.dr1', '144.el1', '144.ep1', '216.ex1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 87222236613, 36933, 87100665], 'label': '6912.ia.72.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fo1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564665
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.ch1', '36.di1', '36.eq1', '36.fk1', '36.fn1', '36.it1'], 'contains': ['144.dr1', '144.en1', '144.fa1', '216.ez1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 87298060748], 'label': '6912.ia.72.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564666
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.ci1', '36.dh1', '36.ep1', '36.fj1', '36.fl1', '36.it1'], 'contains': ['144.dr1', '144.em1', '144.ez1', '144.na1', '144.oa1', '216.ey1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87261772748, 83480268], 'label': '6912.ia.72.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fp1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564667
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.cg1', '36.dk1', '36.eq1', '36.fi1', '36.fl1', '36.is1'], 'contains': ['144.dr1', '144.eo1', '144.eu1', '144.nb1', '144.oc1', '216.fa1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 93405312000, 36933, 87265400268, 40279680], 'label': '6912.ia.72.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fr1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564668
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.cf1', '36.di1', '36.es1', '36.fi1', '36.fm1', '36.iu1'], 'contains': ['144.dr1', '144.eq1', '144.ew1', '144.nc1', '144.od1', '216.fb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87261771468, 83481548], 'label': '6912.ia.72.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fs1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564669
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '36.cg1', '36.dh1', '36.er1', '36.fh1', '36.fo1', '36.iu1'], 'contains': ['144.dr1', '144.er1', '144.ex1', '216.fc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.72.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ft1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564670
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.ch1', '36.dj1', '36.er1', '36.fj1', '36.fm1', '36.iv1'], 'contains': ['144.dr1', '144.ey1', '144.fb1', '144.my1', '144.ny1', '216.fd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 36933, 87178291946], 'label': '6912.ia.72.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565550
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '8.j1', '8.l1', '8.n1'], 'contains': ['32.i1', '48.e1', '48.dx1', '48.dy1', '48.dz1', '64.c1'], 'core': '48.e1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 47537280, 36933, 746], 'label': '6912.ia.16.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564671
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '36.v1', '36.ci1', '36.dk1', '36.es1', '36.fn1', '36.fo1', '36.iv1'], 'contains': ['144.dr1', '144.ev1', '144.fc1', '144.my1', '144.nd1', '144.nx1', '144.oe1', '216.fe1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 87218571626, 36933, 40279680], 'label': '6912.ia.72.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564672
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '36.e1', '36.cj1', '36.ct1', '36.ej1', '36.fp1', '36.fq1', '36.iw1'], 'contains': ['144.fr1', '144.ne1', '144.oh1', '216.fe1', '288.u1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40297548, 87218571626, 36933, 2676, 40279680], 'label': '6912.ia.72.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564673
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.p1', '6.q1', '6.r1', '6.s1', '6.u1', '6.v1', '6.z1', '6.ba1', '6.bb1', '6.bc1', '6.bf1', '6.bg1', '6.bm1', '6.bn1', '9.b1', '9.c1', '12.ds1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.3.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '3.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564674
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1', '4.i1'], 'contains': ['24.de1', '24.df1', '24.dg1', '24.dh1', '24.di1', '24.dl1', '24.dm1', '24.du1', '24.dv1', '24.dx1', '24.dy1', '24.ef1', '24.eg1', '24.eo1', '24.ep1', '36.jy1', '36.ka1'], 'core': '144.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87178291200, 36933, 47537280, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.12.ds1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '12.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ds1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243564675
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '36.ck1', '36.fr1', '36.ix1'], 'contains': ['144.fs1', '144.nf1', '144.oi1', '216.fe1', '288.v1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40312609, 40297548, 87218571626, 36933, 93405314676, 40279680], 'label': '6912.ia.72.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '72.hs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564676
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.bp1', '36.fs1', '36.ft1', '36.fu1', '36.fv1', '36.id1'], 'contains': ['144.ds1', '144.dt1', '144.dx1', '144.ef1', '144.el1', '216.ff1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 87222236613, 36933, 87100665], 'label': '6912.ia.72.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ht1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564677
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.bv1', '36.dn1', '36.ep1', '36.ex1', '36.fs1', '36.iy1'], 'contains': ['144.dx1', '144.ek1', '144.ez1', '144.nh1', '144.nk1', '216.fg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.72.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564678
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '36.bx1', '36.dm1', '36.eq1', '36.fa1', '36.fs1', '36.iz1'], 'contains': ['144.dx1', '144.en1', '144.eu1', '216.fi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 93405312000, 36933, 87100665], 'label': '6912.ia.72.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gb1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564679
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.by1', '36.dl1', '36.ep1', '36.ez1', '36.ft1', '36.iz1'], 'contains': ['144.dx1', '144.em1', '144.et1', '144.ni1', '144.nj1', '216.fh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 83480268], 'label': '6912.ia.72.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ga1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564680
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '36.bw1', '36.do1', '36.eq1', '36.ey1', '36.ft1', '36.iy1'], 'contains': ['144.dx1', '144.eo1', '144.fa1', '144.no1', '216.fj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.72.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564681
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.bv1', '36.dm1', '36.es1', '36.ey1', '36.fu1', '36.ja1'], 'contains': ['144.dx1', '144.eq1', '144.ev1', '144.nl1', '144.nm1', '216.fk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 87261771468], 'label': '6912.ia.72.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gd1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564682
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '36.bw1', '36.dl1', '36.er1', '36.ex1', '36.fv1', '36.ja1'], 'contains': ['144.dx1', '144.er1', '144.ey1', '216.fl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 7656719, 9465, 93405312000, 36933, 87100665], 'label': '6912.ia.72.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.hz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ge1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564683
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '36.bx1', '36.dn1', '36.er1', '36.ez1', '36.fu1', '36.jb1'], 'contains': ['144.dx1', '144.ex1', '144.fb1', '144.np1', '216.fm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 7621226, 36933], 'label': '6912.ia.72.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ia1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gf1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564684
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '36.be1', '36.by1', '36.do1', '36.es1', '36.fa1', '36.fv1', '36.jb1'], 'contains': ['144.dx1', '144.ew1', '144.fc1', '144.ng1', '144.nn1', '216.fn1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.72.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ib1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564685
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '6.h1', '6.i1'], 'contains': ['24.m1', '24.p1', '24.y1', '36.bn1', '36.bu1', '48.n1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.12.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564686
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '36.g1', '36.bz1', '36.cu1', '36.ej1', '36.ff1', '36.fw1', '36.jc1'], 'contains': ['144.fr1', '144.nq1', '216.fn1', '288.x1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32929, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ic1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564687
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '36.cx1', '36.fx1', '36.fy1', '36.fz1', '36.ga1', '36.gz1'], 'contains': ['144.dz1', '144.ea1', '144.ef1', '144.ei1', '144.ej1', '216.fo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 93405312000, 43945413, 36933, 87100665], 'label': '6912.ia.72.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.id1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gi1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564688
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '36.cl1', '36.da1', '36.et1', '36.fs1', '36.fx1', '36.is1'], 'contains': ['144.ef1', '144.ek1', '144.eu1', '144.nz1', '144.oc1', '216.fp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 93405312000, 87218588748, 36933, 40279680], 'label': '6912.ia.72.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ie1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564689
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.cn1', '36.cz1', '36.eu1', '36.fs1', '36.ga1', '36.it1'], 'contains': ['144.ef1', '144.en1', '144.ez1', '216.fr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 87261772748], 'label': '6912.ia.72.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.if1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564690
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '36.co1', '36.cy1', '36.et1', '36.ft1', '36.fz1', '36.it1'], 'contains': ['144.ef1', '144.em1', '144.fa1', '144.of1', '216.fq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87298060748, 83480268], 'label': '6912.ia.72.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ig1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gk1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564691
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.cm1', '36.db1', '36.eu1', '36.ft1', '36.fy1', '36.is1'], 'contains': ['144.ef1', '144.eo1', '144.et1', '144.ob1', '144.oc1', '216.fs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 19148, 36933, 87265400268, 40279680], 'label': '6912.ia.72.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ih1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564692
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '36.cl1', '36.cz1', '36.ew1', '36.fu1', '36.fy1', '36.iu1'], 'contains': ['144.ef1', '144.eq1', '144.ex1', '144.og1', '216.ft1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87261771468, 119769548], 'label': '6912.ia.72.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ii1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gn1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564693
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.cm1', '36.cy1', '36.ev1', '36.fv1', '36.fx1', '36.iu1'], 'contains': ['144.ef1', '144.er1', '144.ew1', '216.fu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.72.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ij1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.go1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564694
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.cn1', '36.da1', '36.ev1', '36.fu1', '36.fz1', '36.iv1'], 'contains': ['144.ef1', '144.ev1', '144.fb1', '144.nx1', '144.ny1', '216.fv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 87218571626, 36933], 'label': '6912.ia.72.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ik1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gp1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564695
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '36.ba1', '36.co1', '36.db1', '36.ew1', '36.fv1', '36.ga1', '36.iv1'], 'contains': ['144.ef1', '144.ey1', '144.fc1', '144.ny1', '144.oe1', '216.fw1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305681228, 40312609, 93405312000, 40297548, 36933, 40279680], 'label': '6912.ia.72.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.il1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gq1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564696
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.h1', '6.x1'], 'contains': ['24.m1', '24.q1', '24.u1', '24.dq1', '24.dr1', '36.by1', '36.bz1', '48.o1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 2676, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.12.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564697
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '36.f1', '36.cp1', '36.cr1', '36.ek1', '36.fw1', '36.gb1', '36.iw1'], 'contains': ['144.fr1', '144.oh1', '216.fw1', '288.z1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305681228, 40312609, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.72.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.im1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564698
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '36.cq1', '36.gc1', '36.ix1'], 'contains': ['144.fs1', '144.oi1', '216.fw1', '288.ba1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87305681228, 40312609, 40297548, 36933, 93405314676, 40279680], 'label': '6912.ia.72.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '72.in1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gs1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564699
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.cf1', '36.dr1', '36.dt1', '36.fb1', '36.fx1', '36.ji1'], 'contains': ['144.ei1', '144.ek1', '144.ew1', '144.ok1', '144.on1', '216.fx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.72.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.io1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gt1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564700
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '36.ch1', '36.dq1', '36.du1', '36.fb1', '36.ga1', '36.jj1'], 'contains': ['144.ei1', '144.en1', '144.ey1', '216.fz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.72.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ip1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gv1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564701
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.ci1', '36.dp1', '36.dt1', '36.fc1', '36.fz1', '36.jj1'], 'contains': ['144.ei1', '144.em1', '144.ev1', '144.ol1', '144.om1', '216.fy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 93405312000, 36933, 87100665, 83480268], 'label': '6912.ia.72.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.iq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gu1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564702
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '36.cg1', '36.ds1', '36.du1', '36.fc1', '36.fy1', '36.ji1'], 'contains': ['144.ei1', '144.eo1', '144.ex1', '144.or1', '216.ga1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.72.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ir1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gw1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564703
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.cf1', '36.dq1', '36.dw1', '36.fd1', '36.fy1', '36.jk1'], 'contains': ['144.ei1', '144.eq1', '144.et1', '144.oo1', '144.op1', '216.gb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 93405312000, 36933, 87100665, 87261771468], 'label': '6912.ia.72.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.is1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564704
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '36.cg1', '36.dp1', '36.dv1', '36.fe1', '36.fx1', '36.jk1'], 'contains': ['144.ei1', '144.er1', '144.eu1', '216.gc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.72.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.it1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564705
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '36.ch1', '36.dr1', '36.dv1', '36.fd1', '36.fz1', '36.jl1'], 'contains': ['144.ei1', '144.fa1', '144.fb1', '144.os1', '216.gd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 36933, 87185912426], 'label': '6912.ia.72.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.iu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gz1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564706
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '36.be1', '36.ci1', '36.ds1', '36.dw1', '36.fe1', '36.ga1', '36.jl1'], 'contains': ['144.ei1', '144.ez1', '144.fc1', '144.oj1', '144.oq1', '216.ge1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.72.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.iv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ha1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564707
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.i1', '6.x1'], 'contains': ['24.m1', '24.s1', '24.z1', '36.cd1', '36.ce1', '48.p1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 2676, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.12.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243564708
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '36.g1', '36.cj1', '36.cv1', '36.ef1', '36.fg1', '36.gb1', '36.jm1'], 'contains': ['144.fr1', '144.ot1', '216.ge1', '288.bc1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 36933, 87185912426, 2676, 87124129, 87109068], 'label': '6912.ia.72.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.iw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564709
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '36.ck1', '36.gc1', '36.jr1'], 'contains': ['144.fs1', '144.oy1', '216.ge1', '288.bd1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [32929, 36933, 87185912426, 93405314676, 87124129, 87109068], 'label': '6912.ia.72.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '72.ix1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564710
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '36.df1', '36.dx1', '36.ex1', '36.fh1', '36.fx1', '36.ha1'], 'contains': ['144.ej1', '144.ek1', '144.er1', '144.fe1', '144.fm1', '216.gf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 119750400, 87265400268, 87124129], 'label': '6912.ia.72.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.iy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hd1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564711
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.dg1', '36.dy1', '36.ey1', '36.fi1', '36.fy1', '36.ha1'], 'contains': ['144.ej1', '144.eo1', '144.eq1', '144.ff1', '144.fq1', '216.gg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 87218588748, 36933, 119750400, 87124129], 'label': '6912.ia.72.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.iz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.he1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564712
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '36.dd1', '36.ed1', '36.ez1', '36.fh1', '36.fy1', '36.hb1'], 'contains': ['144.ej1', '144.et1', '144.ex1', '216.gh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.72.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ja1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243564713
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '36.de1', '36.dz1', '36.fa1', '36.fi1', '36.fx1', '36.hb1'], 'contains': ['144.ej1', '144.eu1', '144.ew1', '216.gi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.72.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hg1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243564714
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '36.de1', '36.dx1', '36.ey1', '36.fn1', '36.fz1', '36.hc1'], 'contains': ['144.ej1', '144.ev1', '144.fa1', '216.gj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 87298060748], 'label': '6912.ia.72.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564715
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '36.dd1', '36.dy1', '36.ex1', '36.fj1', '36.ga1', '36.hc1'], 'contains': ['144.ej1', '144.ey1', '144.ez1', '216.gk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 87261772748], 'label': '6912.ia.72.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564716
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.df1', '36.dz1', '36.ez1', '36.fj1', '36.fz1', '36.hd1'], 'contains': ['144.ej1', '144.em1', '144.fb1', '144.fd1', '144.fi1', '216.gl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 40297548, 36933], 'label': '6912.ia.72.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.je1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hj1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564717
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '36.bt1', '36.ea1', '36.fb1', '36.fk1', '36.fs1', '36.ie1'], 'contains': ['144.ek1', '144.el1', '144.en1', '144.fk1', '144.fm1', '216.gm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43926348, 36933, 87265400268, 87124129], 'label': '6912.ia.72.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hk1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564718
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.i1', '6.y1'], 'contains': ['24.m1', '24.t1', '24.w1', '24.ds1', '24.dt1', '36.ci1', '36.cj1', '36.ck1', '48.q1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87185912426, 2676, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.12.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564719
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bm1', '36.ca1', '36.dr1', '36.dx1', '36.et1', '36.fk1', '36.iy1'], 'contains': ['144.ek1', '144.ep1', '144.fa1', '216.gn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.72.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hl1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564720
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bm1', '36.cl1', '36.dn1', '36.ea1', '36.el1', '36.fh1', '36.ji1'], 'contains': ['144.ek1', '144.es1', '144.ex1', '216.go1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.72.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564721
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.bu1', '36.eb1', '36.fc1', '36.fl1', '36.ft1', '36.ie1'], 'contains': ['144.el1', '144.em1', '144.eo1', '144.fo1', '144.fp1', '216.gp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 87218588748, 36933, 87124129, 83480268], 'label': '6912.ia.72.hn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ji1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hn1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564722
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '36.br1', '36.ee1', '36.fd1', '36.fk1', '36.ft1', '36.if1'], 'contains': ['144.el1', '144.et1', '144.fa1', '216.gq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222236613, 36933, 87100665, 87298060748], 'label': '6912.ia.72.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ho1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564723
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '36.bs1', '36.ec1', '36.fe1', '36.fl1', '36.fs1', '36.if1'], 'contains': ['144.el1', '144.eu1', '144.ez1', '216.gr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222236613, 36933, 87100665, 87261772748], 'label': '6912.ia.72.hp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564724
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '36.bs1', '36.ea1', '36.fc1', '36.fo1', '36.fu1', '36.ig1'], 'contains': ['144.el1', '144.ev1', '144.ex1', '216.gs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222236613, 36933, 87100665, 119769548], 'label': '6912.ia.72.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564725
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '36.br1', '36.eb1', '36.fb1', '36.fm1', '36.fv1', '36.ig1'], 'contains': ['144.el1', '144.ew1', '144.ey1', '216.gt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222236613, 36933, 87100665, 83481548], 'label': '6912.ia.72.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564726
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.bt1', '36.ec1', '36.fd1', '36.fm1', '36.fu1', '36.ih1'], 'contains': ['144.el1', '144.eq1', '144.fb1', '144.fh1', '144.fj1', '216.he1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 87222199680, 36933], 'label': '6912.ia.72.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ic1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564727
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '36.cc1', '36.dq1', '36.ed1', '36.eu1', '36.fk1', '36.iz1'], 'contains': ['144.en1', '144.ep1', '144.et1', '216.gw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.72.hu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hu1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564728
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '36.cn1', '36.dm1', '36.ea1', '36.em1', '36.fn1', '36.jj1'], 'contains': ['144.en1', '144.es1', '144.ev1', '216.gx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 87222200426, 36933, 87100665], 'label': '6912.ia.72.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564729
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.h1', '6.y1'], 'contains': ['24.m1', '24.v1', '24.ba1', '36.co1', '36.cp1', '36.cq1', '48.r1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.12.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564730
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '36.cd1', '36.dp1', '36.dz1', '36.et1', '36.fl1', '36.iz1'], 'contains': ['144.em1', '144.ep1', '144.eu1', '216.gu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 83480268], 'label': '6912.ia.72.hs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hs1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564731
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '36.co1', '36.dl1', '36.eb1', '36.el1', '36.fj1', '36.jj1'], 'contains': ['144.em1', '144.es1', '144.ey1', '216.gv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222200426, 36933, 87100665, 83480268], 'label': '6912.ia.72.ht1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ht1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564732
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '36.cb1', '36.ds1', '36.dy1', '36.eu1', '36.fl1', '36.iy1'], 'contains': ['144.eo1', '144.ep1', '144.ez1', '216.gy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.72.hw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.js1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hw1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564733
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '36.cm1', '36.do1', '36.eb1', '36.em1', '36.fi1', '36.ji1'], 'contains': ['144.eo1', '144.es1', '144.ew1', '216.gz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.72.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hx1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564734
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '36.ca1', '36.dq1', '36.dy1', '36.ew1', '36.fm1', '36.ja1'], 'contains': ['144.ep1', '144.eq1', '144.ey1', '216.ha1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 87261771468], 'label': '6912.ia.72.hy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ju1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564735
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '36.cb1', '36.dp1', '36.dx1', '36.ev1', '36.fo1', '36.ja1'], 'contains': ['144.ep1', '144.er1', '144.ev1', '216.hb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.72.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564736
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '36.cl1', '36.dm1', '36.ec1', '36.eo1', '36.fi1', '36.jk1'], 'contains': ['144.eq1', '144.es1', '144.eu1', '216.hc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222200426, 36933, 87100665, 87261771468], 'label': '6912.ia.72.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ia1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564737
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '36.cm1', '36.dl1', '36.ee1', '36.en1', '36.fh1', '36.jk1'], 'contains': ['144.er1', '144.es1', '144.et1', '216.hd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87298059468, 9465, 93405312000, 87222200426, 36933, 87100665], 'label': '6912.ia.72.ib1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ib1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564738
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '36.cc1', '36.dr1', '36.dz1', '36.ev1', '36.fm1', '36.jb1'], 'contains': ['144.ep1', '144.ew1', '144.fb1', '216.hf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 93405312000, 40297548, 36933], 'label': '6912.ia.72.id1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.id1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564739
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '36.cn1', '36.dn1', '36.ec1', '36.en1', '36.fj1', '36.jl1'], 'contains': ['144.es1', '144.ez1', '144.fb1', '216.hg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 87222200426, 40297548, 36933], 'label': '6912.ia.72.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.jz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ie1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564740
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.h1', '6.j1'], 'contains': ['24.p1', '24.q1', '24.v1', '24.eb1', '24.ed1', '36.cr1', '36.db1', '48.s1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.12.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564741
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1', '36.bl1', '36.dg1', '36.ed1', '36.fa1', '36.fn1', '36.ga1', '36.hd1'], 'contains': ['144.ej1', '144.en1', '144.fc1', '216.hh1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.72.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ka1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.if1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564742
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '36.bl1', '36.bu1', '36.ee1', '36.fe1', '36.fo1', '36.fv1', '36.ih1'], 'contains': ['144.el1', '144.er1', '144.fc1', '216.hi1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87222199680, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.72.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.kb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ig1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564743
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '36.bm1', '36.cd1', '36.ds1', '36.ed1', '36.ew1', '36.fo1', '36.jb1'], 'contains': ['144.ep1', '144.ex1', '144.fc1', '216.hj1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.72.ih1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.kc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ih1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564744
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '36.bm1', '36.co1', '36.do1', '36.ee1', '36.eo1', '36.fn1', '36.jl1'], 'contains': ['144.es1', '144.fa1', '144.fc1', '216.hk1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.72.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.kd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ii1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564745
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.df1', '36.ha1'], 'contains': ['144.fe1', '144.fd1', '144.ff1', '144.fg1', '144.fl1', '144.fj1', '144.fp1', '216.hl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87218603809, 93405312000, 40297548, 36933, 119750400], 'label': '6912.ia.72.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.ke1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ij1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564746
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '36.bt1', '36.ie1'], 'contains': ['144.fk1', '144.fg1', '144.fl1', '144.fh1', '144.fo1', '144.fi1', '144.fq1', '216.hm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87218603809, 93405312000, 40297548, 36933, 83495329], 'label': '6912.ia.72.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.kf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ik1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564747
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1', '36.h1', '36.cs1', '36.eg1', '36.ff1', '36.fp1', '36.gb1', '36.he1'], 'contains': ['144.fr1', '216.hh1', '288.bq1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.il1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.kg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.il1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564748
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '36.h1', '36.bn1', '36.eh1', '36.fg1', '36.fq1', '36.fw1', '36.ib1'], 'contains': ['144.fr1', '216.hi1', '288.br1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87222199680, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.kh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.im1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564749
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '36.i1', '36.ce1', '36.cv1', '36.eg1', '36.ek1', '36.fq1', '36.jc1'], 'contains': ['144.fr1', '216.hj1', '288.bs1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43909226, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ki1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.in1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564750
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '36.i1', '36.cp1', '36.cu1', '36.eh1', '36.ei1', '36.fp1', '36.jm1'], 'contains': ['144.fr1', '216.hk1', '288.bt1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.72.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.kj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.io1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564751
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '6.j1', '6.k1'], 'contains': ['24.p1', '24.r1', '24.x1', '36.cs1', '36.dg1', '48.t1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87218570880, 93405312000, 32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.12.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564752
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1', '36.fr1', '36.gc1', '36.hf1'], 'contains': ['144.fs1', '216.hh1', '288.bu1'], 'core': '864.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [32929, 43908480, 36933, 93405314676, 87124129, 87109068], 'label': '6912.ia.72.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.y1', 'old_label': '72.kk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ip1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564753
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '36.cq1', '36.fr1', '36.jr1'], 'contains': ['144.fs1', '216.hk1', '288.bv1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [32929, 87222200426, 36933, 93405314676, 87124129, 87109068], 'label': '6912.ia.72.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '72.kl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iq1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564754
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '24.bo1', '36.gp1', '36.gx1', '36.gy1'], 'contains': ['144.w1', '144.y1', '144.cd1', '144.cx1', '144.fw1', '144.fz1', '144.gl1', '144.po1', '144.qx1', '216.hs1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.72.jf1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.km1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243564755
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bs1', '24.bm1', '24.bp1', '36.gd1'], 'contains': ['144.x1', '144.z1', '144.ck1', '144.df1', '144.fx1', '144.gc1', '144.gm1', '144.pp1', '144.qy1', '216.hs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 36933, 2676, 40279680], 'label': '6912.ia.72.jg1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '72.kn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564756
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '24.bq1', '36.gp1', '36.gx1', '36.gz1'], 'contains': ['144.ba1', '144.bd1', '144.dj1', '144.dz1', '144.fw1', '144.gi1', '144.gp1', '144.pq1', '144.qz1', '216.ht1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.72.jh1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ko1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564757
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bv1', '24.bn1', '24.br1', '36.gd1'], 'contains': ['144.bb1', '144.be1', '144.dn1', '144.eb1', '144.fx1', '144.gj1', '144.gq1', '144.pr1', '144.ra1', '216.ht1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 127370880, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.72.ji1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.kp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ji1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564758
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bw1', '24.bn1', '24.bs1'], 'contains': ['144.bc1', '144.bf1', '144.dp1', '144.ec1', '144.fy1', '144.gk1', '144.gs1', '144.ps1', '144.rb1', '216.ht1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 127370880, 87222200426, 36933, 93405314676, 40279680], 'label': '6912.ia.72.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '72.kq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564759
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1', '36.gq1', '36.gy1', '36.gz1', '36.ha1', '36.hb1', '36.hc1', '36.hd1'], 'contains': ['144.bg1', '144.bh1', '144.ej1', '144.fd1', '144.fw1', '144.gw1', '144.gy1', '216.hu1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 36933, 40279680], 'label': '6912.ia.72.jk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.kr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jk1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243564760
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '36.gq1', '36.gx1', '36.ha1'], 'contains': ['144.bi1', '144.bj1', '144.fe1', '144.ff1', '144.fw1', '144.gx1', '144.gz1', '216.hv1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 87218603809, 93405312000, 36933, 40279680], 'label': '6912.ia.72.jl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ks1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564761
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '24.bp1', '36.ge1', '36.hg1', '36.hh1'], 'contains': ['144.b1', '144.ga1', '144.gn1', '144.rc1', '216.hs1', '288.di1'], 'core': '144.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.72.jm1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '72.kt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564762
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.i1', '6.k1'], 'contains': ['24.p1', '24.s1', '24.t1', '24.ec1', '24.ed1', '36.ct1', '36.dk1', '48.u1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.12.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564763
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1', '24.br1', '24.bs1', '36.ge1', '36.hg1', '36.hi1'], 'contains': ['144.b1', '144.gh1', '144.gr1', '144.rd1', '216.ht1', '288.dj1'], 'core': '144.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.72.jn1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.ku1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564764
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1', '36.b1', '36.gf1', '36.hh1', '36.hi1', '36.hj1', '36.hk1', '36.hl1'], 'contains': ['144.b1', '144.ha1', '144.hc1', '216.hu1', '288.dk1'], 'core': '144.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 47537280, 36933, 40279680], 'label': '6912.ia.72.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.kv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564766
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '24.ca1', '36.gp1', '36.hn1', '36.ho1'], 'contains': ['144.by1', '144.ce1', '144.cp1', '144.da1', '144.fz1', '144.ge1', '144.gp1', '144.pt1', '144.re1', '216.hw1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.72.jq1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.kx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564767
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '24.cb1', '36.ge1', '36.hm1', '36.hp1'], 'contains': ['144.ga1', '144.gf1', '144.gr1', '144.rf1', '216.hw1', '288.dz1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87185911680, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.72.jr1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.ky1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564768
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '24.cc1', '36.hq1'], 'contains': ['144.gb1', '144.gg1', '144.gt1', '144.rg1', '216.hw1', '288.ea1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87185911680, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.72.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.hq1', 'old_label': '72.kz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.js1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564769
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.gh1', '36.hg1', '36.hm1'], 'contains': ['144.ga1', '144.gh1', '144.hb1', '216.hx1', '288.ec1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40280426, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.72.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.la1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jt1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564770
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.gs1', '36.gx1', '36.hn1'], 'contains': ['144.bz1', '144.cb1', '144.cw1', '144.cz1', '144.fz1', '144.gi1', '144.gx1', '216.hx1'], 'core': '288.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 36933, 87305671545, 40279680], 'label': '6912.ia.72.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '72.lb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ju1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243564771
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '36.gr1', '36.gy1', '36.hn1'], 'contains': ['144.ca1', '144.cf1', '144.cy1', '144.dc1', '144.fz1', '144.gl1', '144.gy1', '216.hy1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.72.jv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.lc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jv1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243564772
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '36.gg1', '36.hh1', '36.hm1'], 'contains': ['144.ga1', '144.gn1', '144.hc1', '216.hy1', '288.ef1'], 'core': '288.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.72.jw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '72.ld1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jw1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564773
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1', '6.h1', '6.k1'], 'contains': ['24.p1', '24.u1', '24.ba1', '36.cu1', '36.do1', '48.v1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 2676, 87218570880, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.12.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564774
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '36.gr1', '36.gx1', '36.ho1'], 'contains': ['144.cc1', '144.cg1', '144.db1', '144.dd1', '144.fz1', '144.gp1', '144.gz1', '216.hz1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 127370880, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.72.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.le1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jx1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564775
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '36.gg1', '36.hg1', '36.hp1'], 'contains': ['144.ga1', '144.gr1', '144.hd1', '216.hz1', '288.ei1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 127370880, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.72.jy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.lf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jy1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564776
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '36.hq1'], 'contains': ['144.gb1', '144.gt1', '144.hf1', '216.hz1', '288.ej1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87298051065, 127370880, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.72.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.hq1', 'old_label': '72.lg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jz1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564777
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.gs1', '36.gy1', '36.ho1', '36.hr1', '36.hs1', '36.ht1', '36.hu1'], 'contains': ['144.ch1', '144.ci1', '144.de1', '144.fz1', '144.gw1', '216.ia1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 36933, 40279680], 'label': '6912.ia.72.ka1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.lh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ka1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243564778
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.gh1', '36.hh1', '36.hp1', '36.hv1', '36.hw1', '36.hx1', '36.hy1'], 'contains': ['144.ga1', '144.ha1', '216.ia1', '288.el1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.72.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.li1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kb1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564779
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.hq1', '36.hz1', '36.ia1'], 'contains': ['144.gb1', '144.he1', '216.ia1', '288.em1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 93452849280, 36933, 40279680], 'label': '6912.ia.72.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bg1', 'old_label': '72.lj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kc1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564780
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cg1', '24.ca1', '24.cb1', '24.cc1', '36.gd1'], 'contains': ['144.cj1', '144.cl1', '144.cm1', '144.dg1', '144.gc1', '144.gd1', '144.gq1', '144.pu1', '144.rh1', '216.hw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87185911680, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.72.kd1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.lk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564781
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ch1', '24.cd1', '24.ce1', '36.gd1'], 'contains': ['144.cn1', '144.co1', '144.do1', '144.dy1', '144.gd1', '144.gj1', '144.gm1', '144.pv1', '144.ri1', '216.ib1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 36933, 2676, 40279680], 'label': '6912.ia.72.ke1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.ll1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ke1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564782
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1', '24.cf1', '36.ge1', '36.hm1', '36.ic1'], 'contains': ['144.gf1', '144.gh1', '144.gn1', '144.rj1', '216.ib1', '288.es1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.72.kf1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.lm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kf1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564783
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1', '24.cf1', '36.gp1', '36.hn1', '36.id1'], 'contains': ['144.cq1', '144.cr1', '144.dk1', '144.ds1', '144.ge1', '144.gi1', '144.gl1', '144.pw1', '144.rk1', '216.ib1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.72.kg1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ln1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564802
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.gt1', '36.gz1', '36.ho1', '36.ji1', '36.jj1', '36.jk1', '36.jl1'], 'contains': ['144.eg1', '144.ei1', '144.es1', '144.gp1', '144.gw1', '216.ij1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.72.kw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.md1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kw1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564784
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1728.cj1', '1728.ci1', '1728.bz1', '1728.by1', '1728.cb1', '1728.ca1', '1728.ch1', '1728.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.bm1', '12.bw1', '16.a1', '16.i1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243564785
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1', '6.i1', '6.j1'], 'contains': ['24.p1', '24.w1', '24.z1', '36.cv1', '36.ds1', '48.w1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 2676, 87218570880, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564786
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.gq1', '36.ho1', '36.id1', '36.ie1', '36.if1', '36.ig1', '36.ih1'], 'contains': ['144.cs1', '144.ct1', '144.el1', '144.fh1', '144.ge1', '144.gw1', '144.gz1', '216.ic1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 36933, 40279680], 'label': '6912.ia.72.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.lo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564787
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1', '36.gq1', '36.hn1', '36.ie1'], 'contains': ['144.cu1', '144.cv1', '144.fk1', '144.fo1', '144.ge1', '144.gx1', '144.gy1', '216.id1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 87218603809, 93405312000, 36933, 40279680], 'label': '6912.ia.72.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.lp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ki1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564788
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.gf1', '36.hp1', '36.ic1', '36.ii1', '36.ij1', '36.ik1', '36.il1'], 'contains': ['144.gf1', '144.ha1', '144.hd1', '216.ic1', '288.ez1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 47537280, 36933, 40279680], 'label': '6912.ia.72.kj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.lq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564789
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1', '36.gf1', '36.hm1', '36.ii1'], 'contains': ['144.gf1', '144.hb1', '144.hc1', '216.id1', '288.fa1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 87218603809, 47537280, 36933, 40279680], 'label': '6912.ia.72.kk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.lr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564790
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.hq1', '36.im1', '36.in1'], 'contains': ['144.gg1', '144.he1', '144.hf1', '216.ic1', '288.fb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93452849280, 36933, 40279680], 'label': '6912.ia.72.kl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '72.ls1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564791
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1', '36.gg1', '36.hg1', '36.ic1'], 'contains': ['144.gh1', '144.gn1', '144.hd1', '216.ie1', '288.fj1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 127370880, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.72.km1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.lt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.km1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564792
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1', '36.gg1', '36.hi1', '36.hm1'], 'contains': ['144.gh1', '144.gr1', '144.hc1', '216.if1', '288.fk1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.72.kn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.lu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kn1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564793
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1', '36.gh1', '36.hi1', '36.ic1', '36.io1', '36.ip1', '36.iq1', '36.ir1'], 'contains': ['144.gh1', '144.ha1', '216.ig1', '288.fl1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.72.ko1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.lv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ko1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564794
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1', '36.gr1', '36.gx1', '36.id1'], 'contains': ['144.dh1', '144.dm1', '144.dt1', '144.ee1', '144.gi1', '144.gl1', '144.gz1', '216.ie1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 127370880, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.72.kp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.lw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564795
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1', '36.gr1', '36.gz1', '36.hn1'], 'contains': ['144.di1', '144.dl1', '144.ea1', '144.ed1', '144.gi1', '144.gp1', '144.gy1', '216.if1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.72.kq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.lx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564796
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.j1', '6.bh1'], 'contains': ['24.q1', '24.r1', '24.w1', '24.eh1', '24.ek1', '36.dw1', '36.ef1', '48.x1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564797
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1', '36.gs1', '36.gz1', '36.id1', '36.is1', '36.it1', '36.iu1', '36.iv1'], 'contains': ['144.dq1', '144.dr1', '144.ef1', '144.gi1', '144.gw1', '216.ig1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87218571626, 36933, 40279680], 'label': '6912.ia.72.kr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.ly1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kr1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243564798
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1', '36.gt1', '36.gx1', '36.hn1'], 'contains': ['144.du1', '144.dw1', '144.eh1', '144.fn1', '144.gl1', '144.gp1', '144.gx1', '216.ih1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 36933, 87305671545, 40279680], 'label': '6912.ia.72.ks1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.lz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ks1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564799
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '36.gt1', '36.gy1', '36.id1', '36.iy1', '36.iz1', '36.ja1', '36.jb1'], 'contains': ['144.dv1', '144.dx1', '144.ep1', '144.gl1', '144.gw1', '216.ii1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.72.kt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ma1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kt1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564800
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1', '36.gi1', '36.hg1', '36.hm1'], 'contains': ['144.gn1', '144.gr1', '144.hb1', '216.ih1', '288.fv1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.72.ku1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.mb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ku1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564801
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '36.gi1', '36.hh1', '36.ic1', '36.jd1', '36.je1', '36.jf1', '36.jg1'], 'contains': ['144.gn1', '144.ha1', '216.ii1', '288.fw1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.72.kv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kv1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564803
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.gi1', '36.hi1', '36.hp1', '36.jn1', '36.jo1', '36.jp1', '36.jq1'], 'contains': ['144.gr1', '144.ha1', '216.ij1', '288.gc1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.72.kx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.me1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kx1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564804
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.hq1', '36.js1', '36.jt1'], 'contains': ['144.gt1', '144.he1', '216.ij1', '288.gd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.72.ky1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '72.mf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ky1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564805
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '36.a1', '36.ha1', '36.hr1', '36.ie1', '36.is1', '36.iy1', '36.ji1'], 'contains': ['144.ek1', '144.eo1', '144.fg1', '144.gw1', '144.gx1', '216.ik1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 87265400268, 40279680], 'label': '6912.ia.72.kz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kz1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243564806
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.gu1', '36.hd1', '36.hs1', '36.ie1', '36.it1', '36.iz1', '36.jj1'], 'contains': ['144.en1', '144.em1', '144.fi1', '144.gw1', '144.gy1', '216.il1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 83480268, 40279680], 'label': '6912.ia.72.la1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.mh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.la1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243564807
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.j1', '6.x1'], 'contains': ['24.q1', '24.x1', '24.z1', '36.ed1', '36.eg1', '48.y1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 43908480, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564808
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.gu1', '36.ha1', '36.ht1', '36.ih1', '36.iu1', '36.ja1', '36.jk1'], 'contains': ['144.eq1', '144.er1', '144.fj1', '144.gw1', '144.gz1', '216.im1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 87261771468, 40279680], 'label': '6912.ia.72.lb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.mi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lb1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243564809
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.lc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.gv1', '36.hb1', '36.hu1', '36.if1', '36.is1', '36.iz1', '36.jk1'], 'contains': ['144.et1', '144.eu1', '144.gw1', '216.in1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 36933, 40279680], 'label': '6912.ia.72.lc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564810
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.gv1', '36.hc1', '36.hr1', '36.ig1', '36.iv1', '36.ja1', '36.jj1'], 'contains': ['144.ev1', '144.ey1', '144.gw1', '216.io1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87305681228, 127370880, 127380345, 93405312000, 36933, 40279680], 'label': '6912.ia.72.ld1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ld1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564811
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '36.gw1', '36.hb1', '36.hs1', '36.ig1', '36.iu1', '36.jb1', '36.ji1'], 'contains': ['144.ew1', '144.ex1', '144.gw1', '216.ip1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 119769548, 40279680], 'label': '6912.ia.72.le1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ml1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.le1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243564812
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.gw1', '36.hc1', '36.ht1', '36.if1', '36.it1', '36.iy1', '36.jl1'], 'contains': ['144.ez1', '144.fa1', '144.gw1', '216.iq1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87298060748, 40279680], 'label': '6912.ia.72.lf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.mm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564813
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '36.gu1', '36.ha1', '36.ie1'], 'contains': ['144.fm1', '144.fl1', '144.fq1', '144.fp1', '144.gx1', '144.gy1', '144.gz1', '216.ir1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87218603809, 93405312000, 36933, 83480268, 40279680], 'label': '6912.ia.72.lg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.mn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243564814
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '36.gn1', '36.hj1', '36.hv1', '36.ii1', '36.io1', '36.jd1', '36.jn1'], 'contains': ['144.ha1', '144.hb1', '216.ik1', '288.gy1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.72.lh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.mo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lh1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564815
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.b1', '36.gk1', '36.hw1', '36.ii1', '36.ip1', '36.je1', '36.jo1'], 'contains': ['144.ha1', '144.hc1', '216.il1', '288.gz1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.72.li1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.li1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564816
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.gk1', '36.hj1', '36.hx1', '36.il1', '36.iq1', '36.jf1', '36.jp1'], 'contains': ['144.ha1', '144.hd1', '216.im1', '288.ha1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.72.lj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.mq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lj1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564817
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.gl1', '36.hk1', '36.hy1', '36.ij1', '36.io1', '36.je1', '36.jp1'], 'contains': ['144.ha1', '216.in1', '288.hb1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 47537280, 36933, 40279680], 'label': '6912.ia.72.lk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564818
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.h1', '6.bh1'], 'contains': ['24.q1', '24.y1', '24.ba1', '36.ee1', '36.eh1', '48.z1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87222200426, 2676, 87222199680, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564819
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.gl1', '36.hl1', '36.hv1', '36.ik1', '36.ir1', '36.jf1', '36.jo1'], 'contains': ['144.ha1', '216.io1', '288.hc1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305681228, 127370880, 127380345, 47537280, 36933, 40279680], 'label': '6912.ia.72.ll1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ms1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ll1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564820
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '36.gm1', '36.hk1', '36.hw1', '36.ik1', '36.iq1', '36.jg1', '36.jn1'], 'contains': ['144.ha1', '216.ip1', '288.hd1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.72.lm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.mt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564821
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.gm1', '36.hl1', '36.hx1', '36.ij1', '36.ip1', '36.jd1', '36.jq1'], 'contains': ['144.ha1', '216.iq1', '288.he1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.72.ln1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.mu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ln1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564822
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '36.gk1', '36.hj1', '36.ii1'], 'contains': ['144.hb1', '144.hc1', '144.hd1', '216.ir1', '288.hg1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87218603809, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.72.lo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1', 'old_label': '72.mv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lo1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564823
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.cy1', '24.cz1', '36.hf1', '36.ix1', '36.jr1'], 'contains': ['144.fs1', '216.a1', '288.bx1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 93405314676, 87109068, 40279680], 'label': '6912.ia.72.lp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '72.mw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564824
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.hz1', '36.in1', '36.js1'], 'contains': ['144.he1', '144.hf1', '216.im1', '288.hi1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40312609, 93452849280, 36933, 87261771468, 40279680], 'label': '6912.ia.72.lq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '72.mx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lq1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243564825
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.ia1', '36.im1', '36.js1'], 'contains': ['144.he1', '216.in1', '288.hj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93452849280, 36933, 40279680], 'label': '6912.ia.72.lr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bg1', 'old_label': '72.my1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564826
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.hz1', '36.im1', '36.jt1'], 'contains': ['144.he1', '216.iq1', '288.hk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 93452849280, 36933, 87298060748, 40279680], 'label': '6912.ia.72.ls1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '72.mz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ls1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564827
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.cx1', '24.cz1', '36.ia1', '36.in1', '36.jt1'], 'contains': ['144.he1', '216.a1', '288.hl1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 40312609, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.72.lt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '72.na1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lt1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243564828
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.cw1', '24.cz1', '36.go1', '36.jh1', '36.ju1'], 'contains': ['216.a1', '288.bz1', '288.hm1', '288.hn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 36933, 87109068, 40279680], 'label': '6912.ia.72.lu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '72.nb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lu1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 243564829
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.k1', '6.bh1'], 'contains': ['24.r1', '24.s1', '24.ba1', '36.ei1', '36.eo1', '48.ba1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 87222200426, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564830
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '24.cx1', '24.cy1', '24.cz1', '36.jv1'], 'contains': ['216.a1', '288.ca1', '288.ho1', '288.hp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93525428474, 40312609, 36933, 87109068, 40279680], 'label': '6912.ia.72.lv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '72.nc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lv1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 243564831
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.d1', '36.kd1', '36.ke1'], 'contains': ['144.jn1', '144.jw1', '144.lm1', '216.js1', '288.cs1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 2676, 87265382400], 'label': '6912.ia.72.nd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.nd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564832
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ne1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1'], 'contains': ['144.iq1', '144.ir1', '144.it1', '144.iu1', '144.iv1', '144.iz1', '144.jb1', '144.jx1', '144.jz1', '144.kb1', '144.kh1', '144.kt1', '144.kv1', '144.lo1', '144.lr1', '216.jm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 7656719, 93405312000, 36933, 87265419333, 87100665], 'label': '6912.ia.72.ne1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '72.ne1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ne1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564833
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.kf1', '36.kg1'], 'contains': ['144.iq1', '144.is1', '144.iw1', '144.ix1', '144.jd1', '144.jz1', '144.ka1', '144.kg1', '144.kw1', '144.kx1', '144.lt1', '216.jn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7621226, 36933, 87265419333], 'label': '6912.ia.72.nf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564834
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ng1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.kh1', '36.ki1'], 'contains': ['144.ir1', '144.is1', '144.iy1', '144.ja1', '144.jc1', '144.kb1', '144.kd1', '144.kg1', '144.ln1', '144.lp1', '144.ls1', '216.jo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87265419333, 83498639], 'label': '6912.ia.72.ng1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ng1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ng1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564835
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.kf1', '36.kh1'], 'contains': ['144.is1', '144.it1', '144.jf1', '144.je1', '144.jm1', '144.ki1', '144.kk1', '144.kq1', '144.lv1', '144.lu1', '144.mc1', '216.jp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87100665, 87124129, 87265382400], 'label': '6912.ia.72.nh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564836
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ni1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.kg1', '36.kh1'], 'contains': ['144.is1', '144.jh1', '144.jk1', '144.kl1', '144.ko1', '144.lx1', '144.ma1', '216.jq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7654690, 36933, 87265419333], 'label': '6912.ia.72.ni1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ni1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ni1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564837
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.kf1', '36.ki1'], 'contains': ['144.is1', '144.ji1', '144.jj1', '144.km1', '144.ko1', '144.ly1', '144.lz1', '216.jr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87265419333, 83496610], 'label': '6912.ia.72.nj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564838
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.p1', '36.kg1', '36.ki1'], 'contains': ['144.is1', '144.jg1', '144.jl1', '144.kk1', '144.kp1', '144.lw1', '144.mb1', '216.js1'], 'core': '288.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 87265382400], 'label': '6912.ia.72.nk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.nk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564839
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.du1', '36.ka1', '36.bv1', '36.kf1'], 'contains': ['144.ix1', '144.jf1', '144.jj1', '144.lb1', '144.le1', '144.nh1', '144.nl1', '216.ju1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 7621226, 36933], 'label': '6912.ia.72.nm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564840
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.k1', '6.bl1'], 'contains': ['24.r1', '24.t1', '24.u1', '24.em1', '24.en1', '36.ej1', '36.es1', '48.bb1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.12.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564841
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.by1', '36.kf1'], 'contains': ['144.ix1', '144.je1', '144.ji1', '144.la1', '144.lc1', '144.ng1', '144.nj1', '216.jt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.72.nl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nl1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243564842
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.bv1', '36.kg1'], 'contains': ['144.ix1', '144.jg1', '144.jk1', '144.ld1', '144.le1', '144.nk1', '144.nm1', '216.jv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7621226, 36933, 87265415329], 'label': '6912.ia.72.nn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nn1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564843
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.no1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '24.dv1', '36.ka1', '36.by1', '36.kg1'], 'contains': ['144.ix1', '144.jh1', '144.jl1', '144.lc1', '144.lf1', '144.ni1', '144.nn1', '216.jw1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.72.no1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.no1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.no1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243564844
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.np1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '24.dw1', '36.jw1', '36.bz1', '36.kd1'], 'contains': ['144.d1', '144.jn1', '144.nq1', '216.jw1', '288.cv1'], 'core': '144.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 32929, 7621226, 36933, 2676], 'label': '6912.ia.72.np1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.np1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.np1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564845
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kc1', '36.bv1', '36.kh1'], 'contains': ['144.ja1', '144.jf1', '144.jk1', '144.ml1', '144.mp1', '144.nh1', '144.nm1', '216.jy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 36933, 83498639], 'label': '6912.ia.72.nr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564846
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.by1', '36.kh1'], 'contains': ['144.ja1', '144.je1', '144.jh1', '144.mj1', '144.mm1', '144.ng1', '144.ni1', '216.jx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.72.nq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243564847
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ns1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.bv1', '36.ki1'], 'contains': ['144.ja1', '144.jg1', '144.jj1', '144.mn1', '144.mp1', '144.nk1', '144.nl1', '216.jz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 83498639, 87265415329], 'label': '6912.ia.72.ns1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ns1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ns1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564848
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '36.kc1', '36.by1', '36.ki1'], 'contains': ['144.ja1', '144.ji1', '144.jl1', '144.mm1', '144.mq1', '144.nj1', '144.nn1', '216.ka1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 83463146], 'label': '6912.ia.72.nt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nt1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243564849
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '36.jx1', '36.bz1', '36.ke1'], 'contains': ['144.jn1', '144.mt1', '144.nq1', '216.ka1', '288.cx1'], 'core': '288.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 2676, 83463146], 'label': '6912.ia.72.nu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.nu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564850
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dx1', '36.ka1', '36.cf1', '36.kh1'], 'contains': ['144.jc1', '144.jf1', '144.jh1', '144.mz1', '144.nc1', '144.ok1', '144.oo1', '216.kc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 7654690, 36933], 'label': '6912.ia.72.nw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564851
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.j1', '6.bl1'], 'contains': ['24.r1', '24.v1', '24.z1', '36.ek1', '36.ew1', '48.bc1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564852
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.ci1', '36.kh1'], 'contains': ['144.jc1', '144.je1', '144.jk1', '144.my1', '144.na1', '144.oj1', '144.om1', '216.kb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.72.nv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564853
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.cf1', '36.ki1'], 'contains': ['144.jc1', '144.jg1', '144.ji1', '144.nb1', '144.nc1', '144.on1', '144.op1', '216.kd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 83496610, 87265415329], 'label': '6912.ia.72.nx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.nx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564854
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ny1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '24.dy1', '36.ka1', '36.ci1', '36.ki1'], 'contains': ['144.jc1', '144.jj1', '144.jl1', '144.na1', '144.nd1', '144.ol1', '144.oq1', '216.ke1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 87185912426], 'label': '6912.ia.72.ny1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ny1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ny1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564855
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '24.dz1', '36.jw1', '36.cj1', '36.ke1'], 'contains': ['144.jn1', '144.ne1', '144.ot1', '216.ke1', '288.cz1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 87185912426, 2676], 'label': '6912.ia.72.nz1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.nz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564856
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '24.ea1', '36.ck1'], 'contains': ['144.jo1', '144.nf1', '144.oy1', '216.ke1', '288.da1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 87185912426, 93405314676], 'label': '6912.ia.72.oa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1', 'old_label': '72.oa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oa1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564857
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kc1', '36.cf1', '36.kf1'], 'contains': ['144.jd1', '144.jf1', '144.ji1', '144.nz1', '144.od1', '144.ok1', '144.op1', '216.kg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 36933, 83496610], 'label': '6912.ia.72.oc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ob1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564858
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ob1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.ci1', '36.kf1'], 'contains': ['144.jd1', '144.je1', '144.jj1', '144.nx1', '144.oa1', '144.oj1', '144.ol1', '216.kf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.72.ob1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.oc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ob1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564859
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.od1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.cf1', '36.kg1'], 'contains': ['144.jd1', '144.jg1', '144.jh1', '144.ob1', '144.od1', '144.on1', '144.oo1', '216.kh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7654690, 36933, 87265415329], 'label': '6912.ia.72.od1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.od1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.od1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564860
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.kc1', '36.ci1', '36.kg1'], 'contains': ['144.jd1', '144.jk1', '144.jl1', '144.oa1', '144.oe1', '144.om1', '144.oq1', '216.ki1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 87261754346], 'label': '6912.ia.72.oe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.oe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oe1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564861
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.of1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.jx1', '36.cj1', '36.kd1'], 'contains': ['144.jn1', '144.oh1', '144.ot1', '216.ki1', '288.dc1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 2676, 87261754346], 'label': '6912.ia.72.of1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.of1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.of1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564862
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.k1', '6.x1'], 'contains': ['24.s1', '24.u1', '24.x1', '36.fa1', '36.ff1', '48.bd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43908480, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.12.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243564863
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.og1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.ck1'], 'contains': ['144.jo1', '144.oi1', '144.oy1', '216.ki1', '288.dd1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 93405314676, 87261754346], 'label': '6912.ia.72.og1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1', 'old_label': '72.og1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.og1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564864
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bx1', '24.du1', '36.jy1'], 'contains': ['144.jq1', '144.js1', '144.ju1', '144.lg1', '144.li1', '144.nr1', '144.nt1', '216.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 47537280, 7621226, 36933], 'label': '6912.ia.72.oh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.oh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564865
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.by1', '24.dv1', '24.dw1', '36.jy1'], 'contains': ['144.jq1', '144.jt1', '144.jv1', '144.lh1', '144.lj1', '144.ns1', '144.nu1', '216.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 32929, 47537280, 7621226, 36933], 'label': '6912.ia.72.oi1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '72.oi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oi1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564866
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bz1', '24.dx1', '36.jy1'], 'contains': ['144.jr1', '144.js1', '144.jt1', '144.mu1', '144.mw1', '144.ou1', '144.ow1', '216.kc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 7654690, 47537280, 36933], 'label': '6912.ia.72.oj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.oj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oj1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564867
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ok1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ca1', '24.dy1', '24.dz1', '24.ea1', '36.jy1'], 'contains': ['144.jr1', '144.ju1', '144.jv1', '144.mv1', '144.mx1', '144.ov1', '144.ox1', '216.ke1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.72.ok1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.ok1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ok1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564868
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ol1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '36.e1', '36.cr1', '36.kd1'], 'contains': ['144.d1', '144.jw1', '144.oh1', '216.km1', '288.dm1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933, 746, 2676], 'label': '6912.ia.72.ol1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ol1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ol1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564869
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.om1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ec1', '36.e1', '36.ct1', '36.ke1'], 'contains': ['144.jw1', '144.mt1', '144.ne1', '216.kq1', '288.dn1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 40280426, 36933, 2676], 'label': '6912.ia.72.om1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.om1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.om1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564870
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.on1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ed1', '36.f1', '36.cr1', '36.ct1'], 'contains': ['144.jw1', '144.mt1', '144.oh1', '216.ku1', '288.do1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933, 2676, 127371626], 'label': '6912.ia.72.on1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.be1', 'old_label': '72.on1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.on1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564871
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '36.g1', '36.kd1', '36.ke1'], 'contains': ['144.jw1', '144.nq1', '144.ot1', '216.kz1', '288.dp1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 32929, 7621226, 36933, 2676, 87265382400], 'label': '6912.ia.72.oo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.oo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564872
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.op1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.da1', '36.kf1'], 'contains': ['144.ka1', '144.ki1', '144.km1', '144.lb1', '144.la1', '144.nz1', '144.nx1', '216.kj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 93405312000, 36933, 746], 'label': '6912.ia.72.op1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.op1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.op1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564873
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.i1', '6.bh1'], 'contains': ['24.s1', '24.w1', '24.y1', '36.fe1', '36.fg1', '48.be1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87185912426, 87222199680, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564874
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.da1', '36.db1'], 'contains': ['144.ka1', '144.kj1', '144.kn1', '144.la1', '144.ld1', '144.ny1', '144.oc1', '216.kk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 746, 87265382400], 'label': '6912.ia.72.oq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.oq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564875
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.or1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.kf1', '36.kg1'], 'contains': ['144.ka1', '144.kk1', '144.ko1', '144.lc1', '144.le1', '144.oa1', '144.od1', '216.kl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87265419333, 83495329, 83496610], 'label': '6912.ia.72.or1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.or1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.or1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564876
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.os1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '36.v1', '36.db1', '36.kg1'], 'contains': ['144.ka1', '144.kl1', '144.kp1', '144.ld1', '144.lf1', '144.ob1', '144.oe1', '216.km1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933, 746], 'label': '6912.ia.72.os1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.os1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.os1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564877
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ot1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.dj1', '36.kh1'], 'contains': ['144.kd1', '144.ki1', '144.kl1', '144.ml1', '144.mj1', '144.mz1', '144.my1', '216.kn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 93405312000, 36933, 127371626], 'label': '6912.ia.72.ot1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ot1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ot1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564878
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ou1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.dj1', '36.dk1'], 'contains': ['144.kd1', '144.kj1', '144.kn1', '144.mk1', '144.mo1', '144.my1', '144.nb1', '216.ko1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 87091946, 87265382400], 'label': '6912.ia.72.ou1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.ou1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ou1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564879
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ov1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.kh1', '36.ki1'], 'contains': ['144.kd1', '144.kk1', '144.ko1', '144.mm1', '144.mp1', '144.na1', '144.nc1', '216.kp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 87265419333, 83495329], 'label': '6912.ia.72.ov1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ov1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ov1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564880
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ow1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ec1', '36.v1', '36.dk1', '36.ki1'], 'contains': ['144.kd1', '144.km1', '144.kp1', '144.mn1', '144.mq1', '144.nb1', '144.nd1', '216.kq1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 40280426, 36933], 'label': '6912.ia.72.ow1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ow1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ow1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564881
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ox1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '36.da1', '36.dj1'], 'contains': ['144.ke1', '144.ki1', '144.kn1', '144.ml1', '144.mk1', '144.nz1', '144.ny1', '216.kr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 93405312000, 40280426, 36933], 'label': '6912.ia.72.ox1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.ox1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ox1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564882
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.db1', '36.dj1'], 'contains': ['144.ke1', '144.kj1', '144.kl1', '144.mj1', '144.mo1', '144.ny1', '144.ob1', '216.ks1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 127371626, 87265382400], 'label': '6912.ia.72.oy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.oy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oy1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564883
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.oz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.da1', '36.dk1'], 'contains': ['144.ke1', '144.kj1', '144.km1', '144.mk1', '144.mn1', '144.nx1', '144.oc1', '216.kt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 40280426, 36933, 87265382400], 'label': '6912.ia.72.oz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.oz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.oz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564884
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.k1', '6.y1'], 'contains': ['24.t1', '24.x1', '24.ba1', '36.fn1', '36.fp1', '36.fr1', '48.bf1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 43908480, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.12.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564885
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ed1', '36.ba1', '36.db1', '36.dk1'], 'contains': ['144.ke1', '144.kn1', '144.kp1', '144.mo1', '144.mq1', '144.oc1', '144.oe1', '216.ku1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933, 127371626], 'label': '6912.ia.72.pa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.pa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pa1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564886
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1'], 'contains': ['144.kf1', '144.kq1', '144.kr1', '144.mr1', '144.ms1', '144.of1', '144.og1', '216.kv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 93405312000, 43942690, 36933, 87265419333, 87100665], 'label': '6912.ia.72.pb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '72.pb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564887
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.kf1', '36.kh1'], 'contains': ['144.kg1', '144.ki1', '144.ko1', '144.nh1', '144.ng1', '144.ok1', '144.oj1', '216.kw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83463146, 87124129, 87109068, 87265382400], 'label': '6912.ia.72.pc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564888
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.kg1', '36.kh1'], 'contains': ['144.kg1', '144.kk1', '144.kl1', '144.ni1', '144.nm1', '144.om1', '144.oo1', '216.kx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87265419333, 83498639, 83495329], 'label': '6912.ia.72.pd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564889
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.kf1', '36.ki1'], 'contains': ['144.kg1', '144.kk1', '144.km1', '144.nj1', '144.nl1', '144.ol1', '144.op1', '216.ky1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7621226, 36933, 87265419333, 83495329], 'label': '6912.ia.72.pe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pe1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564890
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '36.be1', '36.kg1', '36.ki1'], 'contains': ['144.kg1', '144.ko1', '144.kp1', '144.nk1', '144.nn1', '144.on1', '144.oq1', '216.kz1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 7621226, 36933, 87265382400], 'label': '6912.ia.72.pf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564891
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1'], 'contains': ['144.kh1', '144.kr1', '144.ks1', '144.no1', '144.np1', '144.or1', '144.os1', '216.la1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 40297548, 36933, 87100665, 83463146, 87265382400], 'label': '6912.ia.72.pg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '72.pg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pg1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564892
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ef1', '36.ka1', '36.dt1', '36.kf1'], 'contains': ['144.kx1', '144.lb1', '144.lc1', '144.lv1', '144.lz1', '144.ok1', '144.ol1', '216.lc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 36933, 83495329, 83496610], 'label': '6912.ia.72.pi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ph1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pi1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564893
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ph1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.dw1', '36.kf1'], 'contains': ['144.kx1', '144.la1', '144.le1', '144.lu1', '144.ly1', '144.oj1', '144.op1', '216.lb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.72.ph1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ph1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564894
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.dt1', '36.kg1'], 'contains': ['144.kx1', '144.lc1', '144.ld1', '144.lw1', '144.ma1', '144.om1', '144.on1', '216.ld1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83495329, 83496610, 87265415329], 'label': '6912.ia.72.pj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pj1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564895
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['1728.cf1', '1728.bj1', '1728.ci1', '1728.cj1', '1728.ch1', '1728.cg1', '1728.bh1', '1728.cd1', '1728.bi1', '1728.cc1', '1728.ce1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1', '2.e1'], 'contains': ['8.a1', '12.c1', '12.d1', '12.bx1', '12.ce1', '16.b1', '16.j1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '12.c1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243564896
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.i1', '6.bl1'], 'contains': ['24.t1', '24.y1', '24.z1', '36.fo1', '36.fq1', '48.bg1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 87222199680, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564897
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eg1', '24.eh1', '36.ka1', '36.dw1', '36.kg1'], 'contains': ['144.kx1', '144.le1', '144.lf1', '144.lx1', '144.mb1', '144.oo1', '144.oq1', '216.le1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 87185912426], 'label': '6912.ia.72.pk1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pk1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564898
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cd1', '24.ef1', '36.jy1'], 'contains': ['144.ky1', '144.lg1', '144.lh1', '144.md1', '144.mf1', '144.ou1', '144.ov1', '216.lc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.72.pl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.pl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pl1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564899
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ce1', '24.eg1', '24.ei1', '36.jy1'], 'contains': ['144.ky1', '144.li1', '144.lj1', '144.me1', '144.mg1', '144.ow1', '144.ox1', '216.le1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.72.pm1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.pm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564900
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cf1', '24.eg1', '24.ej1'], 'contains': ['144.kz1', '144.lk1', '144.ll1', '144.mh1', '144.mi1', '144.oz1', '144.pa1', '216.le1'], 'core': '864.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 93452849280, 36933, 87185912426], 'label': '6912.ia.72.pn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '72.pn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pn1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564901
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.po1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eh1', '24.ei1', '24.ej1', '36.jw1', '36.ef1', '36.kd1'], 'contains': ['144.d1', '144.lm1', '144.ot1', '216.le1', '288.en1'], 'core': '144.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 87185912426, 2676], 'label': '6912.ia.72.po1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.po1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.po1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564902
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ek1', '36.jx1', '36.ef1', '36.ke1'], 'contains': ['144.lm1', '144.mt1', '144.ot1', '216.li1', '288.eo1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 2676, 87261754346], 'label': '6912.ia.72.pp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.pp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564903
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.el1', '24.em1', '36.jw1', '36.ej1', '36.ke1'], 'contains': ['144.lm1', '144.ne1', '144.nq1', '216.lm1', '288.ep1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 7621226, 36933, 2676], 'label': '6912.ia.72.pq1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.pq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564904
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.en1', '36.jx1', '36.ej1', '36.kd1'], 'contains': ['144.lm1', '144.nq1', '144.oh1', '216.lq1', '288.eq1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 2676, 83463146], 'label': '6912.ia.72.pr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.pr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564905
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kc1', '36.dt1', '36.kh1'], 'contains': ['144.lp1', '144.lv1', '144.ma1', '144.ml1', '144.mm1', '144.ok1', '144.om1', '216.lg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 7654690, 36933, 83495329], 'label': '6912.ia.72.pt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.ps1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pt1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564906
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ps1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.dw1', '36.kh1'], 'contains': ['144.lp1', '144.lu1', '144.lx1', '144.mj1', '144.mp1', '144.oj1', '144.oo1', '216.lf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.72.ps1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ps1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564907
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.h1', '6.bl1'], 'contains': ['24.u1', '24.v1', '24.y1', '36.fv1', '36.fw1', '48.bh1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87222199680, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.12.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564908
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.dt1', '36.ki1'], 'contains': ['144.lp1', '144.lw1', '144.lz1', '144.mm1', '144.mn1', '144.ol1', '144.on1', '216.lh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 83495329, 87265415329], 'label': '6912.ia.72.pu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pu1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564909
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ek1', '36.kc1', '36.dw1', '36.ki1'], 'contains': ['144.lp1', '144.ly1', '144.mb1', '144.mp1', '144.mq1', '144.op1', '144.oq1', '216.li1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 87261754346], 'label': '6912.ia.72.pv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564910
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ci1', '24.eo1', '36.jy1'], 'contains': ['144.lq1', '144.md1', '144.me1', '144.mu1', '144.mv1', '144.nr1', '144.ns1', '216.lk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.72.pw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.pw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564911
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.px1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cj1', '24.el1', '24.ep1', '36.jy1'], 'contains': ['144.lq1', '144.mf1', '144.mg1', '144.mw1', '144.mx1', '144.nt1', '144.nu1', '216.lm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 47537280, 7621226, 36933], 'label': '6912.ia.72.px1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.px1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.px1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564912
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.pz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eo1', '36.ka1', '36.ep1', '36.kh1'], 'contains': ['144.ls1', '144.lv1', '144.lx1', '144.mz1', '144.na1', '144.nh1', '144.ni1', '216.lk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 36933, 83498639, 83495329], 'label': '6912.ia.72.pz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.py1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.pz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564913
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.py1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.es1', '36.kh1'], 'contains': ['144.ls1', '144.lu1', '144.ma1', '144.my1', '144.nc1', '144.ng1', '144.nm1', '216.lj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 36933, 87109068, 93405312000, 87124129, 7621226], 'label': '6912.ia.72.py1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.pz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.py1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564914
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '36.ep1', '36.ki1'], 'contains': ['144.ls1', '144.lw1', '144.ly1', '144.na1', '144.nb1', '144.nj1', '144.nk1', '216.ll1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7621226, 36933, 83495329, 87265415329], 'label': '6912.ia.72.qa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qa1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564915
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.em1', '24.ep1', '36.ka1', '36.es1', '36.ki1'], 'contains': ['144.ls1', '144.lz1', '144.mb1', '144.nc1', '144.nd1', '144.nl1', '144.nn1', '216.lm1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 36933, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.72.qb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564916
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kc1', '36.ep1', '36.kf1'], 'contains': ['144.lt1', '144.lv1', '144.ly1', '144.nh1', '144.nj1', '144.nz1', '144.oa1', '216.lo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 7621226, 36933, 83495329], 'label': '6912.ia.72.qd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564917
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.es1', '36.kf1'], 'contains': ['144.lt1', '144.lu1', '144.lz1', '144.ng1', '144.nl1', '144.nx1', '144.od1', '216.ln1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 83463146, 36933, 87109068, 93405312000, 87124129], 'label': '6912.ia.72.qc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564918
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.j1', '6.y1'], 'contains': ['24.v1', '24.w1', '24.x1', '36.ga1', '36.gb1', '36.gc1', '48.bi1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87185912426, 43908480, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564919
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '36.ep1', '36.kg1'], 'contains': ['144.lt1', '144.lw1', '144.lx1', '144.ni1', '144.nk1', '144.oa1', '144.ob1', '216.lp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83498639, 83495329, 87265415329], 'label': '6912.ia.72.qe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qe1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564920
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.en1', '36.kc1', '36.es1', '36.kg1'], 'contains': ['144.lt1', '144.ma1', '144.mb1', '144.nm1', '144.nn1', '144.od1', '144.oe1', '216.lq1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 83463146], 'label': '6912.ia.72.qf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.qf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243564921
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.eq1', '36.gd1'], 'contains': ['144.pi1', '144.pj1', '144.pk1', '144.px1', '144.py1', '144.pz1', '144.qa1', '144.pp1', '144.pr1', '144.pu1', '144.pv1', '144.qp1', '144.qq1', '144.qt1', '144.qu1', '216.lr1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 40316613, 43909226, 87178291200, 2676, 127407813], 'label': '6912.ia.72.qg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.qg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564922
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.er1', '24.es1', '36.gd1'], 'contains': ['144.px1', '144.py1', '144.pz1', '144.qa1', '144.qb1', '144.qe1', '144.qf1', '144.qp1', '144.qq1', '144.qt1', '144.qu1', '144.qy1', '144.ra1', '144.rh1', '144.ri1', '216.ls1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 87178328133, 2676, 40279680], 'label': '6912.ia.72.qi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.qh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564923
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.er1', '24.et1', '36.ge1'], 'contains': ['144.qc1', '144.qd1', '144.qg1', '144.rc1', '144.rd1', '144.rf1', '144.rj1', '216.ls1', '288.js1'], 'core': '288.f1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 7657413, 47537280, 43944719, 87178328133, 40279680], 'label': '6912.ia.72.qj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '72.qi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564924
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.eq1', '36.gp1'], 'contains': ['144.pl1', '144.pm1', '144.pn1', '144.qi1', '144.qj1', '144.qk1', '144.ql1', '144.po1', '144.pq1', '144.pt1', '144.pw1', '144.qr1', '144.qs1', '144.qv1', '144.qw1', '216.lr1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200, 7657413, 43944719, 127407813], 'label': '6912.ia.72.qh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '72.qj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564925
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.qk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.es1', '24.et1', '36.gp1'], 'contains': ['144.qi1', '144.qj1', '144.qk1', '144.ql1', '144.qm1', '144.qn1', '144.qo1', '144.qr1', '144.qs1', '144.qv1', '144.qw1', '144.qx1', '144.qz1', '144.re1', '144.rk1', '216.ls1'], 'core': '288.e1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 43944719, 87178328133, 40279680], 'label': '6912.ia.72.qk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '72.qk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.qk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564926
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1', '48.bq1', '48.bx1', '48.cc1', '48.cg1', '48.cm1', '48.cn1', '48.co1', '48.cp1'], 'contains': ['192.a1', '288.a1', '288.b1', '288.by1', '384.b1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.96.a1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.a1', 'normal_contained_in': ['24.c1', '48.a1', '48.b1', '48.c1'], 'normal_contains': ['192.a1', '288.a1', '288.b1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564927
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': ['72.qj1'], 'conjugacy_class_count': 1, 'contained_in': ['32.i1', '48.d1', '48.e1', '48.f1', '48.bj1', '48.dh1', '48.dr1', '48.ea1', '48.ei1', '48.ep1', '48.ex1', '48.ey1'], 'contains': ['288.c1', '288.d1', '288.hh1', '384.a1'], 'core': '96.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 2676], 'label': '6912.ia.96.b1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.b1', 'normal_contained_in': ['24.b1', '48.d1', '48.e1', '48.f1'], 'normal_contains': ['288.c1', '288.d1'], 'normalizer': '1.a1', 'old_label': '96.b1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564928
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': ['72.pr1', '72.pq1', '72.np1', '72.nu1', '72.of1', '72.nz1', '72.og1', '72.oa1', '72.po1', '72.pp1'], 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '48.a1', '48.g1', '48.fz1', '48.gc1'], 'contains': ['192.a1', '288.e1', '288.jo1', '384.k1'], 'core': '96.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 87178328133, 40279680], 'label': '6912.ia.96.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': ['48.a1', '48.g1'], 'normal_contains': ['192.a1', '288.e1'], 'normalizer': '1.a1', 'old_label': '96.c1', 'projective_image': '6912.ia', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564929
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.o1', '6.x1', '6.y1'], 'contains': ['24.b1', '24.m1', '24.x1', '36.hd1', '36.he1', '36.hf1', '48.bn1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.bx1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243564930
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': ['72.pq1', '72.pr1', '72.oo1', '72.me1', '72.mi1', '72.mh1', '72.mc1', '72.om1', '72.md1', '72.ol1', '72.on1', '72.pp1', '72.po1'], 'conjugacy_class_count': 2, 'contained_in': ['32.l1', '48.b1', '48.g1', '48.gk1', '48.gm1'], 'contains': ['192.a1', '288.f1', '288.lx1', '384.o1'], 'core': '96.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 47537280, 40279680], 'label': '6912.ia.96.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.d1', 'normal_contained_in': ['48.b1', '48.g1'], 'normal_contains': ['192.a1', '288.f1'], 'normalizer': '1.a1', 'old_label': '96.d1', 'projective_image': '6912.ia', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564931
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': ['72.me1', '72.oo1', '72.mi1', '72.mh1', '72.nu1', '72.np1', '72.nz1', '72.of1', '72.oa1', '72.og1', '72.mc1', '72.md1', '72.ol1', '72.om1', '72.on1'], 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '48.c1', '48.g1', '48.gp1', '48.gv1'], 'contains': ['192.a1', '288.mf1', '288.mg1', '288.mh1', '384.z1'], 'core': '96.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 87185948613, 40279680], 'label': '6912.ia.96.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': ['48.c1', '48.g1'], 'normal_contains': ['192.a1'], 'normalizer': '1.a1', 'old_label': '96.e1', 'projective_image': '6912.ia', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.e1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243564932
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '24.da1', '32.b1', '48.cq1'], 'contains': ['192.c1', '192.i1', '192.q1', '192.bz1', '288.cb1', '288.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 120115956, 87178291200, 47537280, 36933], 'label': '6912.ia.96.z1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564933
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.db1', '32.c1', '48.cq1'], 'contains': ['192.c1', '192.n1', '192.v1', '192.ca1', '288.cd1', '288.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.96.ba1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564934
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '24.dc1', '32.d1', '48.cq1'], 'contains': ['192.c1', '192.bb1', '192.bg1', '192.cb1', '288.cg1', '288.ch1', '288.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43576538, 87178291200, 79833600, 36933, 83468087], 'label': '6912.ia.96.bb1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564935
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '48.h1', '48.i1', '48.j1', '48.k1', '48.l1', '48.m1', '48.bl1'], 'contains': ['192.d1', '192.b1', '192.k1', '192.cc1', '192.bo1', '288.g1', '288.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.96.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564936
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1', '32.b1', '48.h1', '48.cs1', '48.ct1'], 'contains': ['192.d1', '192.g1', '192.p1', '192.cd1', '288.cb1', '288.cl1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 2676], 'label': '6912.ia.96.bc1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564937
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '32.b1', '48.cu1', '48.cv1'], 'contains': ['192.e1', '192.h1', '192.s1', '192.ce1', '288.cc1', '288.cl1'], 'core': '576.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 47537280, 36933], 'label': '6912.ia.96.bd1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '96.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564938
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '32.c1', '48.cu1', '48.cw1', '48.cx1'], 'contains': ['192.e1', '192.l1', '192.u1', '192.cf1', '288.cd1', '288.cm1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.96.be1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564939
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '32.c1', '48.i1', '48.cs1'], 'contains': ['192.d1', '192.m1', '192.x1', '192.cg1', '288.ce1', '288.cm1'], 'core': '576.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 746, 2676], 'label': '6912.ia.96.bf1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564940
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1'], 'contains': ['24.bo1', '24.bq1', '24.bu1', '24.bw1', '24.by1', '24.ci1', '24.cl1', '36.gx1', '36.hg1', '48.di1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 87305671545, 7620480], 'label': '6912.ia.12.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '12.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243564941
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '48.i1', '48.j1', '48.ct1'], 'contains': ['192.d1', '192.t1', '192.bc1', '192.ch1', '288.cf1', '288.cn1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 40280426, 87178291200, 36933, 2676], 'label': '6912.ia.96.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564942
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1', '32.d1', '48.k1', '48.cs1', '48.ct1'], 'contains': ['192.d1', '192.y1', '192.bd1', '192.ci1', '288.cg1', '288.co1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 93405312000, 87178291200, 36933, 83468087], 'label': '6912.ia.96.bh1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564943
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '32.d1', '48.cu1', '48.cw1', '48.cy1'], 'contains': ['192.e1', '192.z1', '192.be1', '192.cj1', '288.ch1', '288.co1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178291200, 79833600, 36933, 83468087], 'label': '6912.ia.96.bi1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564944
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '24.dn1', '24.do1', '32.d1'], 'contains': ['192.f1', '192.ba1', '192.bf1', '192.ck1', '288.ci1', '288.co1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 87178291200, 43561327, 36933, 83468087], 'label': '6912.ia.96.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '96.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564945
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '48.cv1', '48.cx1', '48.cy1', '48.cz1', '48.da1', '48.db1', '48.dc1'], 'contains': ['192.e1', '192.bk1', '192.bl1', '288.cj1', '288.cp1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.96.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564946
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '48.cv1', '48.cw1', '48.cz1'], 'contains': ['192.e1', '192.bm1', '192.bn1', '288.ck1', '288.cr1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291200, 79833600, 36933, 83495329], 'label': '6912.ia.96.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564947
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '48.h1', '48.n1', '48.o1', '48.p1', '48.q1', '48.r1', '48.bn1'], 'contains': ['192.b1', '192.g1', '192.cl1', '192.bp1', '288.i1', '288.j1', '288.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.96.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243564948
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '48.bl1', '48.n1', '48.s1', '48.t1', '48.u1', '48.v1', '48.w1'], 'contains': ['192.b1', '192.k1', '192.cm1', '192.bq1', '288.l1', '288.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87305662080, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.96.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564949
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '48.i1', '48.o1', '48.s1', '48.x1', '48.y1', '48.z1', '48.br1'], 'contains': ['192.b1', '192.m1', '192.t1', '192.cn1', '192.br1', '288.n1', '288.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 2676, 40279680], 'label': '6912.ia.96.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564950
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '48.h1', '48.t1', '48.x1', '48.ba1', '48.bb1', '48.bc1', '48.bu1'], 'contains': ['192.b1', '192.p1', '192.co1', '192.bs1', '288.p1', '288.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.96.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564951
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.z1', '6.ba1'], 'contains': ['24.bo1', '24.bt1', '24.bx1', '24.bz1', '24.cm1', '36.gy1', '36.hh1', '48.dj1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 127380345, 7620480], 'label': '6912.ia.12.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243564952
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '48.j1', '48.p1', '48.u1', '48.ba1', '48.bd1', '48.be1', '48.br1'], 'contains': ['192.b1', '192.t1', '192.cp1', '192.bt1', '288.r1', '288.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 36933, 40310618, 87096887, 40279680], 'label': '6912.ia.96.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564953
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '48.i1', '48.q1', '48.u1', '48.bb1', '48.bf1', '48.bg1', '48.ca1'], 'contains': ['192.b1', '192.x1', '192.bc1', '192.cq1', '192.bu1', '288.t1', '288.u1', '288.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87218571626, 36933, 2676, 40279680], 'label': '6912.ia.96.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564954
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '48.k1', '48.o1', '48.v1', '48.bb1', '48.bd1', '48.bh1', '48.cb1'], 'contains': ['192.b1', '192.y1', '192.cr1', '192.bv1', '288.w1', '288.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.96.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564955
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '48.j1', '48.r1', '48.s1', '48.bc1', '48.bh1', '48.bi1', '48.ca1'], 'contains': ['192.b1', '192.bc1', '192.cs1', '192.bw1', '288.y1', '288.z1', '288.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 36933, 40310618, 87265388087, 40279680], 'label': '6912.ia.96.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564956
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '48.k1', '48.q1', '48.w1', '48.x1', '48.be1', '48.bi1', '48.cf1'], 'contains': ['192.b1', '192.bd1', '192.ct1', '192.bx1', '288.bb1', '288.bc1', '288.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.96.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564957
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1', '48.l1', '48.t1', '48.y1', '48.bd1', '48.bf1', '48.bi1', '48.bn1'], 'contains': ['192.b1', '192.cu1', '288.bf1', '288.bq1', '288.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.96.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243564958
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '48.l1', '48.n1', '48.z1', '48.be1', '48.bg1', '48.bh1', '48.bu1'], 'contains': ['192.b1', '192.cv1', '288.bi1', '288.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87222199680, 36933, 2676, 87091200], 'label': '6912.ia.96.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564959
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '48.m1', '48.p1', '48.w1', '48.y1', '48.bc1', '48.bg1', '48.cb1'], 'contains': ['192.b1', '192.cw1', '288.bm1', '288.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.96.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564960
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '48.m1', '48.r1', '48.v1', '48.z1', '48.ba1', '48.bf1', '48.cf1'], 'contains': ['192.b1', '192.cx1', '288.bp1', '288.bt1', '288.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.96.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564961
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '32.a1', '48.bl1', '48.bn1', '48.br1', '48.bu1', '48.ca1', '48.cb1', '48.cf1'], 'contains': ['192.b1', '192.by1', '192.cy1', '288.a1', '288.bw1', '288.bx1'], 'core': '288.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.96.t1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564962
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.bb1', '6.bc1'], 'contains': ['24.bq1', '24.bt1', '24.cj1', '24.ck1', '24.cn1', '36.gz1', '36.hi1', '48.dk1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 47537280, 40279680, 127370880, 87222200426, 93405312000, 127380345, 7620480], 'label': '6912.ia.12.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564963
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '32.a1', '48.bm1', '48.cd1', '48.ch1'], 'contains': ['192.cz1', '288.a1', '288.bz1', '288.ca1', '384.c1'], 'core': '288.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 36933, 40279680], 'label': '6912.ia.96.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '96.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564964
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '32.a1', '48.bk1', '48.bo1', '48.bs1', '48.bv1', '48.by1', '48.ce1', '48.ci1'], 'contains': ['192.da1', '288.b1', '288.bw1', '288.bz1', '384.d1'], 'core': '288.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.96.v1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564965
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '32.a1', '48.bt1', '48.bw1', '48.cj1'], 'contains': ['192.db1', '288.bw1', '288.by1', '288.ca1', '384.e1'], 'core': '864.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 36933, 40279680], 'label': '6912.ia.96.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1', 'old_label': '96.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564966
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '32.a1', '48.bp1', '48.bz1', '48.ck1'], 'contains': ['192.dc1', '288.b1', '288.bx1', '288.ca1', '384.f1'], 'core': '288.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93525427956, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.96.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '96.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243564967
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1', '32.a1', '48.cl1'], 'contains': ['192.dd1', '288.bx1', '288.by1', '288.bz1', '288.ca1', '384.g1'], 'core': '864.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 93452849280, 36933, 40279680], 'label': '6912.ia.96.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '96.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243564968
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '48.h1', '48.df1', '48.dg1'], 'contains': ['192.g1', '192.k1', '192.p1', '192.de1', '288.cs1', '288.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 2676, 87265382400], 'label': '6912.ia.96.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564969
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '32.e1', '48.cs1', '48.o1', '48.df1'], 'contains': ['192.g1', '192.m1', '192.y1', '192.df1', '288.cu1', '288.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 2676], 'label': '6912.ia.96.bn1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564970
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '48.ct1', '48.o1', '48.dg1'], 'contains': ['192.g1', '192.t1', '192.y1', '192.dg1', '288.cw1', '288.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 36933, 83468087], 'label': '6912.ia.96.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243564971
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '32.f1', '48.cs1', '48.q1', '48.dg1'], 'contains': ['192.g1', '192.x1', '192.bd1', '192.dh1', '288.cy1', '288.cz1', '288.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87185912426, 2676], 'label': '6912.ia.96.bp1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564972
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '48.ct1', '48.q1', '48.df1'], 'contains': ['192.g1', '192.bc1', '192.bd1', '192.di1', '288.db1', '288.dc1', '288.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 36933, 87261759287], 'label': '6912.ia.96.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564973
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.z1', '6.bb1'], 'contains': ['24.bt1', '24.bu1', '24.co1', '24.cq1', '24.cv1', '36.ha1', '36.hj1', '48.dl1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.12.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243564974
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '32.e1', '48.cu1', '48.di1', '48.dj1'], 'contains': ['192.h1', '192.l1', '192.z1', '192.dj1', '288.cu1', '288.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.96.br1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564975
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '24.dw1', '32.e1', '48.cq1'], 'contains': ['192.i1', '192.n1', '192.bb1', '192.dk1', '288.cv1', '288.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 47537280, 7621226, 36933], 'label': '6912.ia.96.bs1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '96.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564976
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1', '32.f1', '48.cu1', '48.di1', '48.dk1'], 'contains': ['192.h1', '192.u1', '192.be1', '192.dl1', '288.cy1', '288.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.96.bt1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564977
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1', '24.dz1', '32.f1', '48.cq1'], 'contains': ['192.i1', '192.v1', '192.bg1', '192.dm1', '288.cz1', '288.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 120115956, 47537280, 36933, 87185912426], 'label': '6912.ia.96.bu1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564978
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1', '24.ea1', '32.f1'], 'contains': ['192.j1', '192.w1', '192.bi1', '192.dn1', '288.da1', '288.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93525427956, 47537280, 36933, 87185912426], 'label': '6912.ia.96.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '96.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564979
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1', '48.cv1', '48.dj1', '48.dk1', '48.dl1', '48.dm1', '48.dn1', '48.do1'], 'contains': ['192.h1', '192.bk1', '192.bm1', '288.de1', '288.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.96.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243564980
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '48.cv1', '48.di1', '48.dl1'], 'contains': ['192.h1', '192.bl1', '192.bn1', '288.dg1', '288.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 87178324129, 47537280, 36933], 'label': '6912.ia.96.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564981
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '48.i1', '48.s1', '48.df1'], 'contains': ['192.k1', '192.m1', '192.bc1', '192.do1', '288.dm1', '288.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 746, 2676], 'label': '6912.ia.96.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.by1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564982
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ec1', '48.i1', '48.u1', '48.dg1'], 'contains': ['192.k1', '192.t1', '192.x1', '192.dp1', '288.dn1', '288.dr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 40280426, 36933, 2676], 'label': '6912.ia.96.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564983
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ed1', '48.j1', '48.s1', '48.u1'], 'contains': ['192.k1', '192.t1', '192.bc1', '192.dq1', '288.do1', '288.ds1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87218570880, 6851, 93405312000, 36933, 87096887], 'label': '6912.ia.96.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '96.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ca1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564984
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.ba1', '6.bb1'], 'contains': ['24.bt1', '24.cr1', '24.ct1', '36.hb1', '36.hk1', '48.dm1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.12.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243564985
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '48.k1', '48.df1', '48.dg1'], 'contains': ['192.k1', '192.y1', '192.bd1', '192.dr1', '288.dp1', '288.dt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 93405312000, 36933, 83468087, 87265382400], 'label': '6912.ia.96.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564986
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '32.g1', '48.cu1', '48.ds1', '48.dt1'], 'contains': ['192.l1', '192.s1', '192.be1', '192.ds1', '288.dy1', '288.dz1', '288.ea1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.96.cc1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243564987
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '48.cx1', '48.di1', '48.ds1'], 'contains': ['192.l1', '192.u1', '192.bl1', '288.ec1', '288.ed1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 36933, 746, 87178300665], 'label': '6912.ia.96.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564988
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '48.cw1', '48.dj1', '48.ds1'], 'contains': ['192.l1', '192.z1', '192.bm1', '288.ee1', '288.ef1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 7621226, 36933, 7629945], 'label': '6912.ia.96.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ce1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243564989
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '48.cw1', '48.di1', '48.dt1'], 'contains': ['192.l1', '192.be1', '192.bn1', '288.eh1', '288.ei1', '288.ej1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 36933, 87185912426, 87185921145], 'label': '6912.ia.96.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243564990
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '48.cx1', '48.dj1', '48.dt1', '48.du1', '48.dv1', '48.dw1', '48.dx1'], 'contains': ['192.l1', '192.bk1', '288.ek1', '288.el1', '288.em1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 47537280, 36933, 746], 'label': '6912.ia.96.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243564991
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eh1', '32.g1', '48.cs1', '48.x1', '48.df1'], 'contains': ['192.m1', '192.p1', '192.bd1', '192.dt1', '288.dy1', '288.en1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87185912426, 2676], 'label': '6912.ia.96.ch1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564992
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '24.ei1', '32.g1', '48.cq1'], 'contains': ['192.n1', '192.q1', '192.bg1', '192.du1', '288.dz1', '288.en1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 87185911680, 47537280, 36933, 87185912426], 'label': '6912.ia.96.ci1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564993
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1', '24.ej1', '32.g1'], 'contains': ['192.o1', '192.r1', '192.bh1', '192.dv1', '288.ea1', '288.en1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [174404119680, 93525427956, 87185911680, 36933, 87185912426], 'label': '6912.ia.96.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '96.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564994
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ek1', '48.ct1', '48.x1', '48.dg1'], 'contains': ['192.p1', '192.t1', '192.bd1', '192.dw1', '288.eo1', '288.er1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 87185911680, 93405312000, 36933, 87261759287], 'label': '6912.ia.96.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564995
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.z1', '6.bc1'], 'contains': ['24.bt1', '24.cs1', '24.cu1', '36.hc1', '36.hl1', '48.dn1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.12.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243564996
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1', '24.el1', '32.h1', '48.cq1'], 'contains': ['192.q1', '192.v1', '192.bb1', '192.dx1', '288.ep1', '288.es1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 87185911680, 47537280, 7621226, 36933], 'label': '6912.ia.96.cl1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564997
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.em1', '32.h1', '48.cs1', '48.bb1', '48.dg1'], 'contains': ['192.p1', '192.x1', '192.y1', '192.dy1', '288.ep1', '288.et1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93405312000, 7621226, 36933, 2676], 'label': '6912.ia.96.cm1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564998
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.en1', '48.ct1', '48.bb1', '48.df1'], 'contains': ['192.p1', '192.y1', '192.bc1', '192.dz1', '288.eq1', '288.eu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 87185911680, 93405312000, 36933, 83468087], 'label': '6912.ia.96.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243564999
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1', '32.h1', '48.cu1', '48.ds1', '48.ed1'], 'contains': ['192.s1', '192.u1', '192.z1', '192.ea1', '288.es1', '288.et1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.96.co1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.co1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565000
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '48.cv1', '48.dt1', '48.ed1', '48.ee1', '48.ef1', '48.eg1', '48.eh1'], 'contains': ['192.s1', '192.bk1', '192.bn1', '288.ev1', '288.ez1', '288.fb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.96.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565001
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1', '48.cv1', '48.ds1', '48.ee1'], 'contains': ['192.s1', '192.bl1', '192.bm1', '288.ex1', '288.fa1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178324129, 79833600, 36933, 83495329], 'label': '6912.ia.96.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565002
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1', '48.cw1', '48.di1', '48.ed1'], 'contains': ['192.u1', '192.z1', '192.bn1', '288.fj1', '288.fm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 7621226, 36933, 87185921145], 'label': '6912.ia.96.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565003
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1', '48.cw1', '48.dk1', '48.ds1'], 'contains': ['192.u1', '192.be1', '192.bm1', '288.fk1', '288.fo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 36933, 87185912426, 7629945], 'label': '6912.ia.96.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565004
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1', '48.cx1', '48.dk1', '48.ed1', '48.ej1', '48.ek1', '48.el1', '48.em1'], 'contains': ['192.u1', '192.bk1', '288.fl1', '288.fp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 47537280, 36933, 87178291946], 'label': '6912.ia.96.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ct1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565005
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1', '48.cy1', '48.di1', '48.ds1'], 'contains': ['192.z1', '192.be1', '192.bl1', '288.fr1', '288.fv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 79833600, 36933, 83468087, 87178300665], 'label': '6912.ia.96.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '96.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565006
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['1728.bj1', '1728.cf1', '1728.bx1', '1728.bg1', '1728.cb1', '1728.ca1', '1728.ci1', '1728.cj1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1', '2.f1'], 'contains': ['8.a1', '12.e1', '12.f1', '12.ck1', '12.cl1', '16.c1', '16.k1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 40280426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.d1', '2.f1'], 'normal_contains': ['8.a1', '12.e1', '12.f1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243565007
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.be1'], 'contains': ['24.cy1', '36.b1', '36.hf1', '48.bp1', '48.dq1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7620480, 93525427956, 127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '12.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565008
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '48.cy1', '48.dj1', '48.ed1', '48.eq1', '48.er1', '48.es1', '48.et1'], 'contains': ['192.z1', '192.bk1', '288.ft1', '288.fw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83498639], 'label': '6912.ia.96.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565009
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '48.cy1', '48.dk1', '48.dt1', '48.ez1', '48.fa1', '48.fb1', '48.fc1'], 'contains': ['192.be1', '192.bk1', '288.ga1', '288.gc1', '288.gd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 87261789839], 'label': '6912.ia.96.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cw1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243565010
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '48.dc1', '48.dl1', '48.du1', '48.ee1', '48.ej1', '48.eq1', '48.ez1'], 'contains': ['192.bk1', '192.bl1', '288.gf1', '288.gy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 47537280, 36933, 87178300665], 'label': '6912.ia.96.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565011
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '48.cz1', '48.do1', '48.dv1', '48.ee1', '48.ek1', '48.er1', '48.fa1'], 'contains': ['192.bk1', '192.bm1', '288.gg1', '288.gz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 79833600, 36933, 83480268], 'label': '6912.ia.96.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cy1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565012
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '48.cz1', '48.dl1', '48.dw1', '48.eh1', '48.el1', '48.es1', '48.fb1'], 'contains': ['192.bk1', '192.bn1', '288.gi1', '288.ha1', '288.hi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 79833600, 36933, 87261771468], 'label': '6912.ia.96.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cz1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243565013
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '48.da1', '48.dm1', '48.dx1', '48.ef1', '48.ej1', '48.er1', '48.fb1'], 'contains': ['192.bk1', '288.gj1', '288.hb1', '288.hj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 47537280, 34210, 36933], 'label': '6912.ia.96.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.da1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565014
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '48.da1', '48.dn1', '48.du1', '48.eg1', '48.em1', '48.es1', '48.fa1'], 'contains': ['192.bk1', '288.gl1', '288.hc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 47537280, 36933, 87178325410], 'label': '6912.ia.96.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.db1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565015
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '48.db1', '48.dm1', '48.dv1', '48.eg1', '48.el1', '48.et1', '48.ez1'], 'contains': ['192.bk1', '288.gm1', '288.hd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 47537280, 36933], 'label': '6912.ia.96.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565016
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '48.db1', '48.dn1', '48.dw1', '48.ef1', '48.ek1', '48.eq1', '48.fc1'], 'contains': ['192.bk1', '288.go1', '288.he1', '288.hk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 47537280, 36933, 87185945890], 'label': '6912.ia.96.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '96.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565017
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '32.i1', '48.dc1', '48.do1', '48.dx1', '48.eh1', '48.em1', '48.et1', '48.fc1'], 'contains': ['192.bk1', '288.c1', '288.hf1', '288.hl1'], 'core': '288.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.96.de1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '96.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.de1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565018
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1'], 'contains': ['24.bv1', '24.bw1', '24.bx1', '24.cf1', '24.ch1', '24.cj1', '24.cl1', '36.hm1', '36.hn1', '48.ds1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.12.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '12.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243565019
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '48.cz1', '48.dl1', '48.ee1'], 'contains': ['192.bl1', '192.bm1', '192.bn1', '288.gw1', '288.hg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178324129, 79833600, 36933, 83480268], 'label': '6912.ia.96.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dg1', 'old_label': '96.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.df1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565020
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '32.i1', '48.dd1', '48.eu1', '48.fd1'], 'contains': ['288.c1', '288.hm1', '288.ho1', '384.c1'], 'core': '288.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 9465, 93405312000, 32929, 36933], 'label': '6912.ia.96.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '96.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565021
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '48.de1', '48.ev1', '48.fe1'], 'contains': ['288.gv1', '288.hn1', '288.hp1', '384.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127388748, 93405312000, 36933, 87124129], 'label': '6912.ia.96.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '96.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565022
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '32.i1', '48.cr1', '48.dp1', '48.dy1', '48.eb1', '48.en1', '48.ew1', '48.ff1'], 'contains': ['288.d1', '288.hf1', '288.hm1', '384.d1'], 'core': '288.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 32929, 47537280, 36933], 'label': '6912.ia.96.di1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '96.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.di1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565023
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '32.i1', '48.dz1', '48.ec1', '48.fg1'], 'contains': ['288.d1', '288.hl1', '288.ho1', '384.e1'], 'core': '288.d1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [174404119680, 93525427956, 9465, 32929, 36933], 'label': '6912.ia.96.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '96.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565024
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '32.i1', '48.dq1', '48.eo1', '48.fh1'], 'contains': ['288.hf1', '288.hh1', '288.ho1', '384.f1'], 'core': '864.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93525427956, 9465, 32929, 47537280, 36933], 'label': '6912.ia.96.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '96.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565025
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1', '32.i1', '48.fi1'], 'contains': ['288.hh1', '288.hl1', '288.hm1', '288.ho1', '384.g1'], 'core': '864.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 9465, 32929, 93452849280, 36933], 'label': '6912.ia.96.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1', 'old_label': '96.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565026
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '48.bk1', '48.fr1', '48.fs1', '48.ft1'], 'contains': ['192.da1', '288.jn1', '288.jo1', '288.jp1', '384.i1'], 'core': '576.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 87178328133, 40279680], 'label': '6912.ia.96.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '96.dm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ed1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565027
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.er1', '32.k1', '48.cq1'], 'contains': ['192.bz1', '192.ca1', '192.cb1', '192.dk1', '192.dm1', '192.du1', '192.dx1', '288.jq1', '288.js1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [7620480, 120115956, 47537280, 7621226, 87178328133], 'label': '6912.ia.96.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '96.dn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ee1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565028
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bl1', '48.fk1', '48.fl1', '48.fm1'], 'contains': ['192.cc1', '192.bo1', '192.by1', '192.cm1', '192.bq1', '288.iq1', '288.ir1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 87178291200, 2676], 'label': '6912.ia.96.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.do1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565029
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.bf1', '6.bg1'], 'contains': ['24.bv1', '24.by1', '24.bz1', '24.cg1', '24.cn1', '36.ho1', '36.hp1', '36.hq1', '48.dt1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 47537280, 40279680, 127370880, 87222200426, 93405312000, 127380345], 'label': '6912.ia.12.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565030
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.h1', '48.fk1', '48.fu1', '48.fv1', '48.fy1'], 'contains': ['192.cc1', '192.cd1', '192.cl1', '192.co1', '192.de1', '288.jh1', '288.jt1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 93405312000, 87178328133, 2676, 87091200], 'label': '6912.ia.96.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.dp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565031
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.i1', '48.fl1', '48.fu1', '48.fw1', '48.ga1'], 'contains': ['192.cc1', '192.cg1', '192.ch1', '192.cn1', '192.cq1', '192.do1', '192.dp1', '288.ji1', '288.ju1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 40280426, 87178328133, 2676, 40279680], 'label': '6912.ia.96.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.dq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565032
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.j1', '48.fl1', '48.fv1', '48.fx1', '48.ga1'], 'contains': ['192.cc1', '192.ch1', '192.cp1', '192.cs1', '192.dq1', '288.jj1', '288.jv1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40304216, 93405312000, 87178291200, 87096887, 40279680], 'label': '6912.ia.96.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.dr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565033
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.k1', '48.fm1', '48.fu1', '48.fx1', '48.gb1'], 'contains': ['192.cc1', '192.ci1', '192.cr1', '192.ct1', '192.dr1', '288.jk1', '288.jw1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.96.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ds1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ei1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565034
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.l1', '48.fk1', '48.fw1', '48.fx1', '48.fy1'], 'contains': ['192.cc1', '192.cu1', '192.cv1', '288.jl1', '288.jx1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 43908480, 87178328133, 2676, 87091200], 'label': '6912.ia.96.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.dt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ej1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565035
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.m1', '48.fm1', '48.fv1', '48.fw1', '48.gb1'], 'contains': ['192.cc1', '192.cw1', '192.cx1', '288.jm1', '288.jy1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43909226, 93405312000, 87178328133, 2676, 87091200], 'label': '6912.ia.96.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.du1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ek1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565036
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '48.bl1', '48.fy1', '48.ga1', '48.gb1'], 'contains': ['192.cc1', '192.cm1', '192.cy1', '288.e1', '288.jn1'], 'core': '288.e1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 93405312000, 87178328133, 2676, 40279680], 'label': '6912.ia.96.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.dv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.el1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565037
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '48.bm1', '48.gd1'], 'contains': ['192.cz1', '288.e1', '288.jp1', '384.l1'], 'core': '288.e1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 87178328133, 40279680], 'label': '6912.ia.96.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '96.dw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.em1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565038
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '48.fj1'], 'contains': ['192.bo1', '192.cd1', '192.bp1', '192.bs1', '192.de1', '288.hq1', '288.hu1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87178291200, 7657413, 87128133, 2676], 'label': '6912.ia.96.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.dx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565039
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.i1', '48.fl1', '48.fj1'], 'contains': ['192.bo1', '192.cg1', '192.ch1', '192.br1', '192.bu1', '192.do1', '192.dp1', '288.hr1', '288.hv1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 93405312000, 40280426, 87178291200, 2676], 'label': '6912.ia.96.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.dy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565040
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1', '6.z1', '6.bf1'], 'contains': ['24.bz1', '24.co1', '24.cs1', '36.hr1', '36.hv1', '48.du1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.12.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565041
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '48.fl1'], 'contains': ['192.bo1', '192.ch1', '192.bt1', '192.bw1', '192.dq1', '288.hs1', '288.hw1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 93405312000, 87105687, 87178328133, 40310618], 'label': '6912.ia.96.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '96.dz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565042
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.k1', '48.fj1'], 'contains': ['192.bo1', '192.ci1', '192.bv1', '192.bx1', '192.dr1', '288.ht1', '288.hx1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87178291200, 24536, 87128133, 83476887], 'label': '6912.ia.96.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.ea1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565043
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.k1', '48.cs1', '48.fu1', '48.fj1'], 'contains': ['192.cd1', '192.cg1', '192.ci1', '192.df1', '192.dh1', '192.dt1', '192.dy1', '288.jq1', '288.jz1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 87178328133, 2676], 'label': '6912.ia.96.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.eb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.en1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565044
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.ct1', '48.fu1', '48.fj1'], 'contains': ['192.cd1', '192.ch1', '192.ci1', '192.dg1', '192.di1', '192.dw1', '192.dz1', '288.jr1', '288.ka1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 87178328133, 83468087], 'label': '6912.ia.96.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.ec1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565045
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.et1', '32.k1', '48.cu1'], 'contains': ['192.ce1', '192.cf1', '192.cj1', '192.dj1', '192.dl1', '192.ds1', '192.ea1', '288.js1', '288.jz1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7620480, 7656719, 93405312000, 47537280, 87178328133], 'label': '6912.ia.96.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '96.ed1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ep1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565046
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bn1', '48.fk1', '48.fn1', '48.fo1'], 'contains': ['192.by1', '192.cl1', '192.cu1', '288.is1', '288.it1', '288.iu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 40316613, 93405312000, 2676, 127407813], 'label': '6912.ia.96.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ee1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dx1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565047
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.br1', '48.fl1', '48.fn1', '48.fp1'], 'contains': ['192.by1', '192.cn1', '192.cp1', '192.br1', '192.bt1', '288.iv1', '288.iw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 40315919, 2676], 'label': '6912.ia.96.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ef1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565048
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bu1', '48.fk1', '48.fp1', '48.fq1'], 'contains': ['192.by1', '192.co1', '192.cv1', '288.ix1', '288.iy1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 87185911680, 93405312000, 2676, 127407813], 'label': '6912.ia.96.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.eg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565049
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ca1', '48.fl1', '48.fo1', '48.fq1'], 'contains': ['192.by1', '192.cq1', '192.cs1', '192.bu1', '192.bw1', '288.iz1', '288.ja1', '288.jb1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 87218571626, 2676], 'label': '6912.ia.96.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.eh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ea1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565050
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cb1', '48.fm1', '48.fn1', '48.fq1'], 'contains': ['192.by1', '192.cr1', '192.cw1', '288.jc1', '288.jd1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 43909226, 93405312000, 2676, 127407813], 'label': '6912.ia.96.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ei1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565051
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '6.ba1', '6.bf1'], 'contains': ['24.bz1', '24.cp1', '24.ct1', '36.hs1', '36.hw1', '48.dv1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.12.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243565052
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cf1', '48.fm1', '48.fo1', '48.fp1'], 'contains': ['192.by1', '192.ct1', '192.cx1', '288.je1', '288.jf1', '288.jg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 87222200426, 2676, 127407813], 'label': '6912.ia.96.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ej1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ec1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565053
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.n1', '48.fk1', '48.fy1', '48.ge1', '48.gf1'], 'contains': ['192.cl1', '192.cm1', '192.cv1', '288.kb1', '288.kc1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 87218607813, 93405312000, 2676, 87091200], 'label': '6912.ia.96.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ek1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565054
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.o1', '48.fu1', '48.fn1', '48.ge1', '48.gi1'], 'contains': ['192.cl1', '192.cn1', '192.cr1', '192.df1', '192.dg1', '288.kd1', '288.ke1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 93405312000, 24536, 83476887, 87091200], 'label': '6912.ia.96.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.el1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.er1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565055
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.p1', '48.fv1', '48.fn1', '48.gf1', '48.gi1'], 'contains': ['192.cl1', '192.cp1', '192.cw1', '288.kf1', '288.kg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43909226, 93405312000, 7657413, 2676, 87091200], 'label': '6912.ia.96.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.em1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.es1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565056
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.q1', '48.fu1', '48.fo1', '48.gf1', '48.gj1'], 'contains': ['192.cl1', '192.cq1', '192.ct1', '192.dh1', '192.di1', '288.kh1', '288.ki1', '288.kj1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 93405312000, 87261768087, 24536, 87091200], 'label': '6912.ia.96.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.en1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.et1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565057
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.r1', '48.fv1', '48.fo1', '48.ge1', '48.gj1'], 'contains': ['192.cl1', '192.cs1', '192.cx1', '288.kk1', '288.kl1', '288.km1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 93405312000, 87222235919, 2676, 87091200], 'label': '6912.ia.96.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.eo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565058
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.s1', '48.fl1', '48.ga1', '48.ge1', '48.gg1'], 'contains': ['192.cm1', '192.cn1', '192.cs1', '192.do1', '192.dq1', '288.kn1', '288.ks1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 40280426, 2676, 87305699013, 40279680], 'label': '6912.ia.96.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ep1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ev1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565059
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.t1', '48.fk1', '48.fy1', '48.gg1', '48.gh1'], 'contains': ['192.cm1', '192.co1', '192.cu1', '288.ko1', '288.kt1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87218607813, 93405312000, 43908480, 2676, 87091200], 'label': '6912.ia.96.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.eq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ew1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565060
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.u1', '48.fl1', '48.ga1', '48.gf1', '48.gh1'], 'contains': ['192.cm1', '192.cp1', '192.cq1', '192.dp1', '192.dq1', '288.kp1', '288.ku1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87305662080, 40304216, 93405312000, 87096887, 40279680], 'label': '6912.ia.96.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.er1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ex1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565061
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.v1', '48.fm1', '48.gb1', '48.ge1', '48.gh1'], 'contains': ['192.cm1', '192.cr1', '192.cx1', '288.kq1', '288.kv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87218607813, 93405312000, 24536, 87091200, 83468087], 'label': '6912.ia.96.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.es1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ey1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565062
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '6.z1', '6.bg1'], 'contains': ['24.bz1', '24.cq1', '24.cu1', '36.ht1', '36.hx1', '36.hz1', '48.dw1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87298060748, 87261771468, 40279680], 'label': '6912.ia.12.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565063
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.w1', '48.fm1', '48.gb1', '48.gf1', '48.gg1'], 'contains': ['192.cm1', '192.ct1', '192.cw1', '288.kr1', '288.kw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87218607813, 43909226, 93405312000, 2676, 87091200], 'label': '6912.ia.96.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.et1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ez1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565064
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.x1', '48.fu1', '48.fp1', '48.gg1', '48.gq1'], 'contains': ['192.cn1', '192.co1', '192.ct1', '192.dt1', '192.dw1', '288.kx1', '288.la1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87185911680, 93405312000, 87261768087, 24536, 87091200], 'label': '6912.ia.96.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.eu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fa1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565065
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.y1', '48.fw1', '48.fn1', '48.gg1', '48.gi1'], 'contains': ['192.cn1', '192.cu1', '192.cw1', '288.ky1', '288.lb1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 43908480, 43944719, 2676, 87091200], 'label': '6912.ia.96.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ev1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565066
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.z1', '48.fw1', '48.fp1', '48.ge1', '48.gq1'], 'contains': ['192.cn1', '192.cv1', '192.cx1', '288.kz1', '288.lc1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87222199680, 87222235919, 2676, 87091200], 'label': '6912.ia.96.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ew1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565067
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ba1', '48.fv1', '48.fp1', '48.gh1', '48.gq1'], 'contains': ['192.co1', '192.cp1', '192.cx1', '288.ld1', '288.lg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87185911680, 93405312000, 87222200426, 2676, 87091200], 'label': '6912.ia.96.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ex1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565068
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bb1', '48.fu1', '48.fq1', '48.gh1', '48.gu1'], 'contains': ['192.co1', '192.cq1', '192.cr1', '192.dy1', '192.dz1', '288.le1', '288.lh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87185911680, 93405312000, 24536, 83476887, 87091200], 'label': '6912.ia.96.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ey1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fe1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565069
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bc1', '48.fv1', '48.fq1', '48.gg1', '48.gu1'], 'contains': ['192.co1', '192.cs1', '192.cw1', '288.lf1', '288.li1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87185911680, 93405312000, 43944719, 2676, 87091200], 'label': '6912.ia.96.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ez1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ff1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565070
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bd1', '48.fx1', '48.fn1', '48.gh1', '48.gi1'], 'contains': ['192.cp1', '192.cr1', '192.cu1', '288.lj1', '288.ll1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 43908480, 24536, 83476887, 87091200], 'label': '6912.ia.96.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fa1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565071
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.be1', '48.fx1', '48.fp1', '48.gf1', '48.gq1'], 'contains': ['192.cp1', '192.ct1', '192.cv1', '288.lk1', '288.lm1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87222236613, 87261768087, 24536, 87091200], 'label': '6912.ia.96.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565072
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bf1', '48.fw1', '48.fo1', '48.gh1', '48.gj1'], 'contains': ['192.cq1', '192.cu1', '192.cx1', '288.ln1', '288.lp1', '288.lr1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 43908480, 87222235919, 2676, 87091200], 'label': '6912.ia.96.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565073
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.s1', '6.ba1', '6.bg1'], 'contains': ['24.c1', '24.bz1', '24.cr1', '36.hu1', '36.hy1', '36.ia1', '48.dx1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.ck1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ck1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243565074
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bg1', '48.fw1', '48.fq1', '48.gf1', '48.gu1'], 'contains': ['192.cq1', '192.cv1', '192.cw1', '288.lo1', '288.lq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87222199680, 43944719, 2676, 87091200], 'label': '6912.ia.96.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565075
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bh1', '48.fx1', '48.fq1', '48.ge1', '48.gu1'], 'contains': ['192.cr1', '192.cs1', '192.cv1', '288.ls1', '288.lt1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87222199680, 24536, 83476887, 87091200], 'label': '6912.ia.96.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fe1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565076
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bi1', '48.fx1', '48.fo1', '48.gg1', '48.gj1'], 'contains': ['192.cs1', '192.ct1', '192.cu1', '288.lu1', '288.lv1', '288.lw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 43908480, 87261768087, 24536, 87091200], 'label': '6912.ia.96.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.ff1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565077
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.l1', '48.bn1', '48.fy1', '48.gi1', '48.gj1'], 'contains': ['192.cl1', '192.cu1', '192.cy1', '288.lx1', '288.ly1', '288.lz1'], 'core': '576.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 2676, 40279680], 'label': '6912.ia.96.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565078
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.l1', '48.bo1', '48.fr1', '48.gl1', '48.gn1'], 'contains': ['192.da1', '288.f1', '288.ly1', '384.p1'], 'core': '288.f1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 47537280, 40279680], 'label': '6912.ia.96.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.fh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565079
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.l1', '48.bp1', '48.go1'], 'contains': ['192.dc1', '288.f1', '288.lz1', '384.q1'], 'core': '288.f1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [93525427956, 127370880, 7657413, 47537280, 40279680], 'label': '6912.ia.96.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '96.fi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565080
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1', '48.bq1', '48.fz1', '48.gk1', '48.gp1'], 'contains': ['192.a1', '288.ma1', '288.mb1', '288.mc1', '384.s1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 47537280, 40279680], 'label': '6912.ia.96.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '96.fj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fp1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565081
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '48.br1', '48.ga1', '48.gi1', '48.gq1'], 'contains': ['192.cn1', '192.cp1', '192.cy1', '288.ma1', '288.md1'], 'core': '576.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 93405312000, 40315919, 2676, 40279680], 'label': '6912.ia.96.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.fk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565082
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '48.bs1', '48.fs1', '48.gl1', '48.gr1'], 'contains': ['192.da1', '288.mb1', '288.md1', '384.u1'], 'core': '576.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 40315919, 40279680], 'label': '6912.ia.96.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.fl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565083
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '48.bt1', '48.gs1'], 'contains': ['192.db1', '288.mc1', '288.md1', '384.v1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40315919, 40279680], 'label': '6912.ia.96.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1', 'old_label': '96.fm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565084
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.bj1'], 'contains': ['24.cx1', '36.c1', '36.ia1', '48.bt1', '48.dz1'], 'core': '36.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40312609, 40280426, 36933, 87109068, 40279680], 'label': '6912.ia.12.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '12.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cl1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565085
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '48.bu1', '48.fy1', '48.gq1', '48.gu1'], 'contains': ['192.co1', '192.cv1', '192.cy1', '288.me1', '288.mf1'], 'core': '576.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 87185948613, 2676, 40279680], 'label': '6912.ia.96.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ft1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565086
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '48.bv1', '48.fr1', '48.gr1', '48.gt1'], 'contains': ['192.da1', '288.me1', '288.mg1', '384.x1'], 'core': '576.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 47537280, 40279680], 'label': '6912.ia.96.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '96.fo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565087
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '48.bw1', '48.gs1'], 'contains': ['192.db1', '288.me1', '288.mh1', '384.y1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87185948613, 40279680], 'label': '6912.ia.96.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '96.fp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565088
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1', '48.bx1', '48.fz1', '48.gm1', '48.gv1'], 'contains': ['192.a1', '288.mi1', '288.mj1', '384.bb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 87218571626, 40279680], 'label': '6912.ia.96.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '96.fq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565089
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.o1', '48.by1', '48.fs1', '48.gn1', '48.gt1'], 'contains': ['192.da1', '288.mi1', '288.mk1', '384.bc1'], 'core': '576.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 87218607119, 40279680], 'label': '6912.ia.96.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '96.fr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565090
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.o1', '48.bz1', '48.go1'], 'contains': ['192.dc1', '288.mi1', '288.ml1', '384.bd1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93525427956, 127370880, 47537280, 87218607119, 40279680], 'label': '6912.ia.96.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '96.fs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565091
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.o1', '48.ca1', '48.ga1', '48.gj1', '48.gu1'], 'contains': ['192.cq1', '192.cs1', '192.cy1', '288.mj1', '288.mk1', '288.ml1'], 'core': '576.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 93405312000, 87218571626, 2676, 40279680], 'label': '6912.ia.96.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.ft1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243565095
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.o1', '6.bh1', '6.bl1'], 'contains': ['24.b1', '24.r1', '24.y1', '36.ib1', '36.ih1', '48.bu1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.cm1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cm1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243565096
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '48.ce1', '48.ft1', '48.gl1', '48.gt1'], 'contains': ['192.da1', '288.mn1', '288.mo1', '288.mp1', '384.bi1'], 'core': '576.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 43944719, 40279680], 'label': '6912.ia.96.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '96.fx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565097
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.cf1', '48.gb1', '48.gj1', '48.gq1'], 'contains': ['192.ct1', '192.cx1', '192.cy1', '288.mq1', '288.mr1', '288.mt1'], 'core': '576.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 2676, 40279680], 'label': '6912.ia.96.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '96.fy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ge1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243565098
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1', '48.cg1', '48.gc1', '48.gm1', '48.gp1'], 'contains': ['192.a1', '288.mq1', '288.ms1', '288.mu1', '384.bl1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 47537280, 40279680], 'label': '6912.ia.96.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '96.fz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565099
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.ch1', '48.gd1'], 'contains': ['192.cz1', '288.mq1', '288.mv1', '288.mw1', '384.bm1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 87222235919, 40279680], 'label': '6912.ia.96.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '96.ga1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565100
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.ci1', '48.ft1', '48.gn1', '48.gr1'], 'contains': ['192.da1', '288.mr1', '288.ms1', '288.mv1', '384.bn1'], 'core': '576.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 87222235919, 40279680], 'label': '6912.ia.96.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '96.gb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565101
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.cj1', '48.gs1'], 'contains': ['192.db1', '288.mr1', '288.mu1', '288.mw1', '384.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87222235919, 40279680], 'label': '6912.ia.96.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '96.gc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565102
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.ck1', '48.go1'], 'contains': ['192.dc1', '288.ms1', '288.mt1', '288.mw1', '384.bp1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93525427956, 127370880, 47537280, 87222235919, 40279680], 'label': '6912.ia.96.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '96.gd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565103
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '48.cl1'], 'contains': ['192.dd1', '288.mt1', '288.mu1', '288.mv1', '288.mw1', '384.bq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120115956, 127370880, 93452849280, 87222235919, 40279680], 'label': '6912.ia.96.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cl1', 'old_label': '96.ge1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gk1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 243565104
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.o1', '48.fj1'], 'contains': ['192.bp1', '192.br1', '192.bv1', '192.df1', '192.dg1', '288.hz1', '288.ia1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 7657413, 24536, 87128133, 83476887], 'label': '6912.ia.96.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565105
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.q1', '48.fj1'], 'contains': ['192.bp1', '192.bu1', '192.bx1', '192.dh1', '192.di1', '288.ib1', '288.ic1', '288.id1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 7657413, 87261768087, 24536, 87128133], 'label': '6912.ia.96.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565106
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.l1', '6.bi1', '6.bk1'], 'contains': ['24.d1', '36.ib1', '36.il1', '48.bv1', '48.eb1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87185911680, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.cn1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cn1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565107
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '48.fl1'], 'contains': ['192.bq1', '192.br1', '192.bw1', '192.do1', '192.dq1', '288.ie1', '288.ig1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 93405312000, 40315919, 2676, 87305699013], 'label': '6912.ia.96.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '96.gh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ds1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565108
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.u1', '48.fl1'], 'contains': ['192.bq1', '192.bt1', '192.bu1', '192.dp1', '192.dq1', '288.if1', '288.ih1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 87305662080, 93405312000, 87105687, 40310618], 'label': '6912.ia.96.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '96.gi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565109
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.x1', '48.fj1'], 'contains': ['192.br1', '192.bs1', '192.bx1', '192.dt1', '192.dw1', '288.ii1', '288.ij1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [24536, 87185948613, 87261768087, 93405312000, 87128133], 'label': '6912.ia.96.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.du1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565110
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bb1', '48.fj1'], 'contains': ['192.bs1', '192.bu1', '192.bv1', '192.dy1', '192.dz1', '288.ik1', '288.il1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87185948613, 24536, 87128133, 83476887], 'label': '6912.ia.96.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565111
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.df1', '48.fu1', '48.fj1'], 'contains': ['192.de1', '192.df1', '192.di1', '192.do1', '192.dr1', '192.dt1', '192.dz1', '288.mx1', '288.mz1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 87265419333, 2676], 'label': '6912.ia.96.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565112
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '96.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.dg1', '48.fu1', '48.fj1'], 'contains': ['192.de1', '192.dg1', '192.dh1', '192.dp1', '192.dr1', '192.dw1', '192.dy1', '288.my1', '288.na1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [6851, 93405312000, 7657413, 87265419333, 83468087], 'label': '6912.ia.96.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '96.gm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565113
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '54.q1'], 'contains': ['216.b1', '216.c1', '216.e1', '216.h1', '216.i1', '216.l1', '216.o1', '216.bh1', '216.bi1', '216.bk1', '216.bn1', '216.cx1', '216.cy1', '216.dq1', '216.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127380345, 43909226, 87178291200, 36933, 87091200], 'label': '6912.ia.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565114
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '54.a1', '54.b1', '54.q1'], 'contains': ['216.b1', '216.d1', '216.f1', '216.j1', '216.p1', '216.is1', '216.it1', '216.iu1', '216.bg1', '216.bj1', '216.bo1', '216.cw1', '216.df1', '216.du1', '216.jm1', '216.jn1', '216.jo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 87178291200, 36933, 87100665], 'label': '6912.ia.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565115
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '54.c1', '54.d1', '54.q1'], 'contains': ['216.c1', '216.d1', '216.m1', '216.n1', '216.t1', '216.bl1', '216.bm1', '216.bp1', '216.dr1', '216.ds1', '216.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 87178291200, 36933, 87100665], 'label': '6912.ia.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565116
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '54.b1', '54.c1', '54.r1'], 'contains': ['216.d1', '216.u1', '216.w1', '216.iw1', '216.ix1', '216.bs1', '216.bu1', '216.dy1', '216.ea1', '216.jq1', '216.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565117
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1728.bj1', '1728.cf1', '1728.by1', '1728.bz1', '1728.cb1', '1728.ca1', '1728.bh1', '1728.bi1', '1728.cc1', '1728.cd1', '1728.ce1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.a1', '12.g1', '12.cm1', '12.cn1', '12.co1', '16.d1', '16.l1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87185911680, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.a1', '12.g1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243565118
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.bj1'], 'contains': ['24.cx1', '36.ib1', '36.in1', '48.bw1', '48.ec1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40312609, 87185911680, 36933, 87109068, 40279680], 'label': '6912.ia.12.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '12.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.co1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565119
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '54.a1', '54.d1', '54.r1'], 'contains': ['216.d1', '216.v1', '216.x1', '216.bt1', '216.bv1', '216.dz1', '216.eb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565120
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '54.a1', '54.c1', '54.s1'], 'contains': ['216.d1', '216.e1', '216.s1', '216.y1', '216.bb1', '216.br1', '216.bw1', '216.by1', '216.dx1', '216.ec1', '216.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 87178291200, 40297548, 36933], 'label': '6912.ia.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565121
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.p1', '54.b1', '54.d1', '54.s1'], 'contains': ['216.d1', '216.r1', '216.z1', '216.iv1', '216.iy1', '216.bq1', '216.bx1', '216.dw1', '216.ed1', '216.jp1', '216.js1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 36933, 87124129, 87109068], 'label': '6912.ia.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565122
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '54.q1'], 'contains': ['216.f1', '216.g1', '216.i1', '216.k1', '216.m1', '216.o1', '216.ba1', '216.db1', '216.dc1', '216.dd1', '216.de1', '216.ef1', '216.eg1', '216.et1', '216.eu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 43909226, 87178291200, 36933, 119750400, 87091200], 'label': '6912.ia.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565123
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '54.e1', '54.f1', '54.q1'], 'contains': ['216.g1', '216.h1', '216.j1', '216.q1', '216.t1', '216.cz1', '216.da1', '216.dg1', '216.di1', '216.ev1', '216.ex1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 87178291200, 43945413, 36933, 87100665], 'label': '6912.ia.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565124
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '54.a1', '54.f1', '54.t1'], 'contains': ['216.j1', '216.s1', '216.x1', '216.dk1', '216.dn1', '216.ez1', '216.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565125
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '54.b1', '54.e1', '54.t1'], 'contains': ['216.j1', '216.r1', '216.w1', '216.ja1', '216.je1', '216.dj1', '216.dm1', '216.ey1', '216.fb1', '216.kl1', '216.kp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565126
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '54.a1', '54.e1', '54.u1'], 'contains': ['216.j1', '216.v1', '216.y1', '216.iz1', '216.jd1', '216.dl1', '216.do1', '216.fa1', '216.fd1', '216.kk1', '216.ko1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87178291200, 40297548, 36933, 746], 'label': '6912.ia.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565127
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.v1', '54.b1', '54.f1', '54.u1'], 'contains': ['216.j1', '216.u1', '216.z1', '216.iz1', '216.jb1', '216.jc1', '216.jf1', '216.dh1', '216.dp1', '216.ew1', '216.fe1', '216.kj1', '216.km1', '216.kn1', '216.kq1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 40280426, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565128
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '54.g1', '54.h1', '54.q1'], 'contains': ['216.k1', '216.l1', '216.n1', '216.p1', '216.q1', '216.eh1', '216.ei1', '216.ej1', '216.ek1', '216.ff1', '216.fo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87178291200, 43945413, 36933, 87100665], 'label': '6912.ia.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565129
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.bm1', '6.bn1'], 'contains': ['24.cf1', '24.cg1', '24.ci1', '24.ck1', '24.cm1', '36.ic1', '36.id1', '48.ed1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 127380345], 'label': '6912.ia.12.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cp1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565130
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '54.c1', '54.h1', '54.t1'], 'contains': ['216.n1', '216.s1', '216.w1', '216.en1', '216.eq1', '216.fr1', '216.fu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565131
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '54.d1', '54.g1', '54.t1'], 'contains': ['216.n1', '216.r1', '216.x1', '216.jg1', '216.em1', '216.ep1', '216.fq1', '216.ft1', '216.kv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565132
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '54.c1', '54.g1', '54.u1'], 'contains': ['216.n1', '216.u1', '216.y1', '216.jc1', '216.jd1', '216.eo1', '216.er1', '216.fs1', '216.fv1', '216.ks1', '216.kt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40280426, 87178291200, 40297548, 36933], 'label': '6912.ia.108.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565133
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '36.ba1', '54.d1', '54.h1', '54.u1'], 'contains': ['216.n1', '216.v1', '216.z1', '216.jd1', '216.jf1', '216.el1', '216.es1', '216.fp1', '216.fw1', '216.kr1', '216.ku1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 127390028, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.108.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565134
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '54.a1', '54.h1', '54.v1'], 'contains': ['216.p1', '216.s1', '216.v1', '216.fi1', '216.fl1', '216.fz1', '216.gc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 87178291200, 36933, 87100665], 'label': '6912.ia.108.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565135
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '54.b1', '54.g1', '54.v1'], 'contains': ['216.p1', '216.r1', '216.u1', '216.ji1', '216.jj1', '216.fh1', '216.fk1', '216.fy1', '216.gb1', '216.kx1', '216.ky1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87178291200, 36933, 87100665, 83480268], 'label': '6912.ia.108.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565136
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '54.a1', '54.g1', '54.w1'], 'contains': ['216.p1', '216.x1', '216.y1', '216.jl1', '216.fj1', '216.fm1', '216.ga1', '216.gd1', '216.la1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.108.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565137
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.be1', '54.b1', '54.h1', '54.w1'], 'contains': ['216.p1', '216.w1', '216.z1', '216.jh1', '216.jk1', '216.fg1', '216.fn1', '216.fx1', '216.ge1', '216.kw1', '216.kz1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87178291200, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.108.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565138
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '54.f1', '54.g1', '54.r1'], 'contains': ['216.q1', '216.u1', '216.x1', '216.gh1', '216.gj1', '216.gq1', '216.gs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.108.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565139
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '54.e1', '54.h1', '54.r1'], 'contains': ['216.q1', '216.v1', '216.w1', '216.gi1', '216.gk1', '216.gr1', '216.gt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.108.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565140
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.bf1', '6.bm1'], 'contains': ['24.cg1', '24.ch1', '24.co1', '24.cp1', '24.cv1', '36.ie1', '36.ii1', '48.ee1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.12.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cq1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565141
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '54.e1', '54.g1', '54.s1'], 'contains': ['216.q1', '216.r1', '216.y1', '216.ba1', '216.bb1', '216.gg1', '216.gl1', '216.gp1', '216.he1', '216.hl1', '216.hm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 87178291200, 40297548, 36933], 'label': '6912.ia.108.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565142
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '54.c1', '54.f1', '54.v1'], 'contains': ['216.s1', '216.t1', '216.u1', '216.gw1', '216.gx1', '216.hb1', '216.hd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 87178291200, 36933, 87100665], 'label': '6912.ia.108.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565143
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1', '54.d1', '54.e1', '54.v1'], 'contains': ['216.r1', '216.t1', '216.v1', '216.gu1', '216.gv1', '216.ha1', '216.hc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 87178291200, 36933, 87100665, 83480268], 'label': '6912.ia.108.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565144
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '54.c1', '54.e1', '54.w1'], 'contains': ['216.t1', '216.w1', '216.y1', '216.gy1', '216.gz1', '216.hf1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 87178291200, 40297548, 36933], 'label': '6912.ia.108.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565145
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '36.bl1', '54.f1', '54.h1', '54.s1'], 'contains': ['216.q1', '216.s1', '216.z1', '216.gf1', '216.gm1', '216.hh1', '216.hi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43908480, 87178291200, 36933, 87124129, 87109068], 'label': '6912.ia.108.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565146
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '36.bm1', '54.d1', '54.f1', '54.w1'], 'contains': ['216.t1', '216.x1', '216.z1', '216.gn1', '216.go1', '216.hj1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43909226, 32929, 87178291200, 36933, 87124129, 87109068], 'label': '6912.ia.108.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565147
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gd1', '36.ge1', '36.gp1', '54.q1'], 'contains': ['216.b1', '216.c1', '216.g1', '216.k1', '216.hn1', '216.ho1', '216.hp1', '216.bc1', '216.bd1', '216.bz1', '216.ce1', '216.hs1', '216.ht1', '216.hw1', '216.ib1', '216.lr1', '216.ls1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.108.eu1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565148
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gf1', '36.gq1', '54.q1', '54.r1', '54.s1'], 'contains': ['216.d1', '216.e1', '216.q1', '216.ba1', '216.hn1', '216.hq1', '216.hr1', '216.be1', '216.bf1', '216.cf1', '216.cg1', '216.hu1', '216.hv1', '216.ic1', '216.id1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87178291200, 36933, 40279680], 'label': '6912.ia.108.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ev1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565149
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gg1', '36.gr1', '54.q1'], 'contains': ['216.f1', '216.h1', '216.l1', '216.m1', '216.ho1', '216.hp1', '216.hr1', '216.ca1', '216.cb1', '216.ch1', '216.ci1', '216.hy1', '216.hz1', '216.ie1', '216.if1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.108.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ew1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565150
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gh1', '36.gs1', '54.q1', '54.t1', '54.u1'], 'contains': ['216.i1', '216.j1', '216.n1', '216.ho1', '216.hq1', '216.cc1', '216.cd1', '216.cj1', '216.hx1', '216.ia1', '216.ig1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.108.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ex1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565151
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.bg1', '6.bm1'], 'contains': ['24.cg1', '24.cr1', '24.cu1', '36.if1', '36.ij1', '36.im1', '48.ef1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93405312000, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.12.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cr1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565152
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gi1', '36.gt1', '54.q1', '54.v1', '54.w1'], 'contains': ['216.o1', '216.p1', '216.t1', '216.hp1', '216.hq1', '216.ck1', '216.cl1', '216.cm1', '216.ih1', '216.ii1', '216.ij1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.108.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ey1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565153
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gk1', '36.gu1', '54.s1', '54.t1', '54.v1'], 'contains': ['216.s1', '216.r1', '216.bb1', '216.hq1', '216.hr1', '216.co1', '216.cn1', '216.cv1', '216.il1', '216.im1', '216.ir1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 36933, 83480268, 40279680], 'label': '6912.ia.108.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ez1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565154
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gl1', '36.gv1', '54.r1', '54.u1', '54.v1'], 'contains': ['216.u1', '216.v1', '216.hq1', '216.cp1', '216.cq1', '216.in1', '216.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 87178291200, 36933, 40279680], 'label': '6912.ia.108.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fa1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565155
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gm1', '36.gw1', '54.r1', '54.t1', '54.w1'], 'contains': ['216.w1', '216.x1', '216.hq1', '216.cr1', '216.cs1', '216.ip1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87178291200, 36933, 119769548, 40279680], 'label': '6912.ia.108.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565156
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.gj1', '36.gn1', '36.go1', '54.s1', '54.u1', '54.w1'], 'contains': ['216.a1', '216.y1', '216.z1', '216.hq1', '216.ct1', '216.cu1', '216.ik1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.108.fc1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565157
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jz1', '54.b1'], 'contains': ['216.it1', '216.iv1', '216.ix1', '216.iz1', '216.ja1', '216.jh1', '216.jj1', '216.jt1', '216.jv1', '216.kb1', '216.kd1', '216.lb1', '216.ld1', '216.lj1', '216.ll1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178291200, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.108.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565158
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jw1', '36.jy1', '36.ka1', '54.b1'], 'contains': ['216.it1', '216.iw1', '216.iy1', '216.ja1', '216.jb1', '216.ji1', '216.jk1', '216.ju1', '216.jw1', '216.kc1', '216.ke1', '216.lc1', '216.le1', '216.lk1', '216.lm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 7621226, 36933], 'label': '6912.ia.108.gi1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gi1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565159
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kb1', '54.b1'], 'contains': ['216.iu1', '216.iv1', '216.iw1', '216.jc1', '216.je1', '216.jh1', '216.ji1', '216.jx1', '216.jz1', '216.kf1', '216.kh1', '216.lf1', '216.lh1', '216.ln1', '216.lp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.108.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565160
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jx1', '36.kc1', '54.b1'], 'contains': ['216.iu1', '216.ix1', '216.iy1', '216.je1', '216.jf1', '216.jj1', '216.jk1', '216.jy1', '216.ka1', '216.kg1', '216.ki1', '216.lg1', '216.li1', '216.lo1', '216.lq1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 36933, 83463146], 'label': '6912.ia.108.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565161
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bo1', '54.q1'], 'contains': ['216.bc1', '216.bd1', '216.bf1', '216.bg1', '216.bi1', '216.bl1', '216.bn1', '216.cb1', '216.cc1', '216.ch1', '216.ck1', '216.da1', '216.de1', '216.ei1', '216.et1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127380345, 43909226, 87305662080, 36933, 87091200], 'label': '6912.ia.108.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565162
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.bf1', '6.bn1'], 'contains': ['24.cg1', '24.cs1', '24.ct1', '36.ig1', '36.ik1', '48.eg1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93405312000, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.12.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cs1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565163
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bp1', '54.q1', '54.i1', '54.j1'], 'contains': ['216.bc1', '216.be1', '216.bh1', '216.bj1', '216.bp1', '216.ca1', '216.cd1', '216.cl1', '216.db1', '216.di1', '216.ff1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 87218607813, 36933, 87100665], 'label': '6912.ia.108.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565164
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1', '54.q1', '54.k1', '54.l1'], 'contains': ['216.bd1', '216.be1', '216.bk1', '216.bm1', '216.bo1', '216.ci1', '216.cj1', '216.cm1', '216.eg1', '216.ek1', '216.ex1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 43909226, 36933, 87100665], 'label': '6912.ia.108.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565165
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bt1', '54.s1', '54.i1', '54.k1'], 'contains': ['216.be1', '216.bf1', '216.bq1', '216.bw1', '216.by1', '216.ct1', '216.co1', '216.cv1', '216.gm1', '216.he1', '216.hm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 87218570880, 40312609, 40297548, 36933], 'label': '6912.ia.108.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565166
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.br1', '54.r1', '54.j1', '54.k1'], 'contains': ['216.be1', '216.bs1', '216.bv1', '216.cp1', '216.cr1', '216.gq1', '216.gt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 36933, 87100665, 83481548], 'label': '6912.ia.108.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565167
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1', '54.r1', '54.i1', '54.l1'], 'contains': ['216.be1', '216.bt1', '216.bu1', '216.cq1', '216.cs1', '216.gr1', '216.gs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 36933, 87100665, 119769548], 'label': '6912.ia.108.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565168
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1', '36.bu1', '54.s1', '54.j1', '54.l1'], 'contains': ['216.be1', '216.br1', '216.bx1', '216.cn1', '216.cu1', '216.gp1', '216.hi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218570880, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.108.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565169
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bv1', '54.b1', '54.i1', '54.x1'], 'contains': ['216.bj1', '216.bq1', '216.bu1', '216.dh1', '216.dm1', '216.fg1', '216.fk1', '216.ju1', '216.jv1', '216.jy1', '216.jz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 36933, 87100665, 87265400268], 'label': '6912.ia.108.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565170
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bw1', '54.a1', '54.j1', '54.x1'], 'contains': ['216.bj1', '216.br1', '216.bv1', '216.dl1', '216.dn1', '216.fj1', '216.fl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 36933, 87100665, 87305679948], 'label': '6912.ia.108.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565171
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bx1', '54.a1', '54.i1', '54.y1'], 'contains': ['216.bj1', '216.bt1', '216.bw1', '216.dk1', '216.do1', '216.fi1', '216.fm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 40297548, 7621226, 36933], 'label': '6912.ia.108.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565172
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.by1', '36.bz1', '54.b1', '54.j1', '54.y1'], 'contains': ['216.bj1', '216.bs1', '216.bx1', '216.dj1', '216.dp1', '216.fh1', '216.fn1', '216.jt1', '216.jw1', '216.jx1', '216.ka1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.108.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565173
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1', '6.bb1', '6.bm1'], 'contains': ['24.ck1', '24.co1', '24.cr1', '36.io1', '36.is1', '48.ej1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.12.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ct1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565174
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ca1', '54.d1', '54.k1', '54.x1'], 'contains': ['216.bm1', '216.bq1', '216.bv1', '216.el1', '216.ep1', '216.gn1', '216.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 36933, 87100665, 87265400268], 'label': '6912.ia.108.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565175
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cb1', '54.c1', '54.l1', '54.x1'], 'contains': ['216.bm1', '216.br1', '216.bu1', '216.eo1', '216.eq1', '216.gy1', '216.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 36933, 87100665, 87305679948], 'label': '6912.ia.108.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565176
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cc1', '54.c1', '54.k1', '54.y1'], 'contains': ['216.bm1', '216.bs1', '216.bw1', '216.en1', '216.er1', '216.gw1', '216.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 43909226, 40297548, 36933], 'label': '6912.ia.108.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.br1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565177
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cd1', '36.ce1', '54.d1', '54.l1', '54.y1'], 'contains': ['216.bm1', '216.bt1', '216.bx1', '216.em1', '216.es1', '216.gu1', '216.hj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 43909226, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.108.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bs1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565178
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1', '54.b1', '54.k1', '54.z1'], 'contains': ['216.bo1', '216.bq1', '216.bs1', '216.ew1', '216.fb1', '216.fx1', '216.gb1', '216.kc1', '216.kd1', '216.kg1', '216.kh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.108.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bt1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565179
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1', '54.a1', '54.l1', '54.z1'], 'contains': ['216.bo1', '216.br1', '216.bt1', '216.fa1', '216.fc1', '216.ga1', '216.gc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.108.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bu1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565180
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ch1', '54.a1', '54.k1', '54.ba1'], 'contains': ['216.bo1', '216.bv1', '216.bw1', '216.ez1', '216.fd1', '216.fz1', '216.gd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 40297548, 36933, 87185912426], 'label': '6912.ia.108.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565181
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ci1', '36.cj1', '36.ck1', '54.b1', '54.l1', '54.ba1'], 'contains': ['216.bo1', '216.bu1', '216.bx1', '216.ey1', '216.fe1', '216.fy1', '216.ge1', '216.kb1', '216.ke1', '216.kf1', '216.ki1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.108.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bw1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565182
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cl1', '54.d1', '54.i1', '54.z1'], 'contains': ['216.bp1', '216.bq1', '216.bt1', '216.fp1', '216.ft1', '216.go1', '216.hc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.108.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565183
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cm1', '54.c1', '54.j1', '54.z1'], 'contains': ['216.bp1', '216.br1', '216.bs1', '216.fs1', '216.fu1', '216.gz1', '216.hd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.108.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565184
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '6.bc1', '6.bm1'], 'contains': ['24.ck1', '24.cp1', '24.cu1', '36.ip1', '36.it1', '48.ek1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87298060748, 83480268, 40279680], 'label': '6912.ia.12.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cu1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565666
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.im1', '48.ef1', '72.pn1'], 'contains': ['288.fb1', '288.hj1', '288.hk1', '432.hz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 87185911680, 93452849280, 36933, 87185945890], 'label': '6912.ia.144.mh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '144.mh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565185
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '54.c1', '54.i1', '54.ba1'], 'contains': ['216.bp1', '216.bu1', '216.bw1', '216.fr1', '216.fv1', '216.gx1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 87222200426, 40297548, 36933], 'label': '6912.ia.108.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565186
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.co1', '36.cp1', '36.cq1', '54.d1', '54.j1', '54.ba1'], 'contains': ['216.bp1', '216.bv1', '216.bx1', '216.fq1', '216.fw1', '216.gv1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.108.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565187
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1', '54.q1'], 'contains': ['216.bz1', '216.ca1', '216.cc1', '216.ce1', '216.cg1', '216.ci1', '216.ck1', '216.cw1', '216.cy1', '216.cz1', '216.dd1', '216.dr1', '216.dt1', '216.eh1', '216.eu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 43909226, 87305662080, 36933, 119750400, 87091200], 'label': '6912.ia.108.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565188
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cx1', '54.q1', '54.m1', '54.n1'], 'contains': ['216.bz1', '216.cb1', '216.cd1', '216.cf1', '216.cm1', '216.cx1', '216.dc1', '216.df1', '216.dg1', '216.dv1', '216.fo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 43945413, 36933, 87100665], 'label': '6912.ia.108.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565189
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.da1', '54.u1', '54.i1', '54.m1'], 'contains': ['216.cd1', '216.ct1', '216.cq1', '216.dh1', '216.do1', '216.fp1', '216.fv1', '216.kj1', '216.kk1', '216.kr1', '216.kt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 40297548, 36933, 746], 'label': '6912.ia.108.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565190
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1', '54.t1', '54.i1', '54.n1'], 'contains': ['216.cd1', '216.co1', '216.cs1', '216.dk1', '216.dm1', '216.fr1', '216.ft1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 36933, 87100665, 119769548], 'label': '6912.ia.108.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565191
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cy1', '54.t1', '54.j1', '54.m1'], 'contains': ['216.cd1', '216.cn1', '216.cr1', '216.dj1', '216.dn1', '216.fq1', '216.fu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.108.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565192
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1', '36.db1', '54.u1', '54.j1', '54.n1'], 'contains': ['216.cd1', '216.cp1', '216.cu1', '216.dl1', '216.dp1', '216.fs1', '216.fw1', '216.kk1', '216.km1', '216.ks1', '216.ku1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 40280426, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.108.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565193
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '54.q1', '54.o1', '54.p1'], 'contains': ['216.ce1', '216.cf1', '216.ch1', '216.cj1', '216.cl1', '216.dq1', '216.ds1', '216.du1', '216.ef1', '216.ej1', '216.ev1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 43945413, 36933, 87100665], 'label': '6912.ia.108.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565194
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.df1', '54.s1', '54.m1', '54.o1'], 'contains': ['216.cf1', '216.cg1', '216.ct1', '216.cn1', '216.cv1', '216.dw1', '216.ec1', '216.ee1', '216.gf1', '216.gl1', '216.hl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43908480, 40297548, 36933], 'label': '6912.ia.108.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ck1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565195
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '6.bb1', '6.bn1'], 'contains': ['24.ck1', '24.cq1', '24.ct1', '36.iq1', '36.iu1', '48.el1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87261771468, 119769548, 40279680], 'label': '6912.ia.12.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cv1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565196
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1', '54.r1', '54.n1', '54.o1'], 'contains': ['216.cf1', '216.cp1', '216.cs1', '216.dy1', '216.eb1', '216.gh1', '216.gk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.108.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ci1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565197
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1', '54.r1', '54.m1', '54.p1'], 'contains': ['216.cf1', '216.cq1', '216.cr1', '216.dz1', '216.ea1', '216.gi1', '216.gj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.108.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565198
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1', '36.dg1', '54.s1', '54.n1', '54.p1'], 'contains': ['216.cf1', '216.co1', '216.cu1', '216.dx1', '216.ed1', '216.gg1', '216.hh1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.108.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cl1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565199
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dj1', '54.u1', '54.k1', '54.o1'], 'contains': ['216.cj1', '216.ct1', '216.cp1', '216.el1', '216.er1', '216.ew1', '216.fd1', '216.kn1', '216.ko1', '216.kr1', '216.ks1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 40280426, 40297548, 36933], 'label': '6912.ia.108.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.co1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565200
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.di1', '54.t1', '54.k1', '54.p1'], 'contains': ['216.cj1', '216.co1', '216.cr1', '216.en1', '216.ep1', '216.ez1', '216.fb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 36933, 87100665, 83481548], 'label': '6912.ia.108.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565201
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dh1', '54.t1', '54.l1', '54.o1'], 'contains': ['216.cj1', '216.cn1', '216.cs1', '216.em1', '216.eq1', '216.ey1', '216.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.108.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565202
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ct1', '36.dk1', '54.u1', '54.l1', '54.p1'], 'contains': ['216.cj1', '216.cq1', '216.cu1', '216.eo1', '216.es1', '216.fa1', '216.fe1', '216.ko1', '216.kq1', '216.kt1', '216.ku1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 127390028, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.108.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cp1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565203
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dn1', '54.w1', '54.i1', '54.o1'], 'contains': ['216.cl1', '216.ct1', '216.cs1', '216.fg1', '216.fm1', '216.go1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 40297548, 7621226, 36933], 'label': '6912.ia.108.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cs1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565204
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1', '54.v1', '54.i1', '54.p1'], 'contains': ['216.cl1', '216.co1', '216.cq1', '216.fi1', '216.fk1', '216.gx1', '216.hc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 87218607813, 36933, 87100665], 'label': '6912.ia.108.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cr1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565205
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1', '54.v1', '54.j1', '54.o1'], 'contains': ['216.cl1', '216.cn1', '216.cp1', '216.fh1', '216.fl1', '216.gv1', '216.hd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 36933, 87100665, 83480268], 'label': '6912.ia.108.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565206
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.s1', '6.bc1', '6.bn1'], 'contains': ['24.c1', '24.ck1', '24.cs1', '36.ir1', '36.iv1', '48.em1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.12.cw1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cw1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565207
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '36.do1', '54.w1', '54.j1', '54.p1'], 'contains': ['216.cl1', '216.cr1', '216.cu1', '216.fj1', '216.fn1', '216.gz1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218570880, 32929, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.108.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ct1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565208
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1', '54.w1', '54.k1', '54.m1'], 'contains': ['216.cm1', '216.ct1', '216.cr1', '216.fx1', '216.gd1', '216.gn1', '216.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43909226, 40297548, 36933], 'label': '6912.ia.108.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cw1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565209
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dq1', '54.v1', '54.k1', '54.n1'], 'contains': ['216.cm1', '216.co1', '216.cp1', '216.fz1', '216.gb1', '216.gw1', '216.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 43909226, 36933, 87100665], 'label': '6912.ia.108.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565210
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1', '54.v1', '54.l1', '54.m1'], 'contains': ['216.cm1', '216.cn1', '216.cq1', '216.fy1', '216.gc1', '216.gu1', '216.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 36933, 87100665, 83480268], 'label': '6912.ia.108.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cu1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565211
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '36.ds1', '54.w1', '54.l1', '54.n1'], 'contains': ['216.cm1', '216.cs1', '216.cu1', '216.ga1', '216.ge1', '216.gy1', '216.hj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218570880, 43909226, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.108.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565212
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dt1', '54.b1', '54.m1', '54.bb1'], 'contains': ['216.df1', '216.dh1', '216.dj1', '216.dw1', '216.ea1', '216.fx1', '216.fy1', '216.lc1', '216.ld1', '216.lg1', '216.lh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87265400268, 83480268, 83481548], 'label': '6912.ia.108.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cy1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565213
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.du1', '54.a1', '54.n1', '54.bb1'], 'contains': ['216.df1', '216.dk1', '216.dl1', '216.dx1', '216.eb1', '216.fz1', '216.ga1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.108.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565214
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dv1', '54.a1', '54.m1', '54.bc1'], 'contains': ['216.df1', '216.dn1', '216.do1', '216.dz1', '216.ec1', '216.gc1', '216.gd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 40297548, 36933, 87185912426], 'label': '6912.ia.108.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.da1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565215
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dw1', '36.ef1', '54.b1', '54.n1', '54.bc1'], 'contains': ['216.df1', '216.dm1', '216.dp1', '216.dy1', '216.ed1', '216.gb1', '216.ge1', '216.lb1', '216.le1', '216.lf1', '216.li1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185911680, 32929, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.108.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.db1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565216
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dx1', '54.f1', '54.m1', '54.x1'], 'contains': ['216.dg1', '216.dh1', '216.dn1', '216.gf1', '216.gj1', '216.gn1', '216.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 43945413, 36933, 87100665, 87265400268], 'label': '6912.ia.108.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565217
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.m1', '6.bd1', '6.bk1'], 'contains': ['24.d1', '36.ir1', '36.iw1', '48.by1', '48.en1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 47537280, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.12.cx1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cx1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565218
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dy1', '54.e1', '54.n1', '54.x1'], 'contains': ['216.dg1', '216.dl1', '216.dm1', '216.gg1', '216.gk1', '216.gy1', '216.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 43945413, 36933, 87100665, 87305679948], 'label': '6912.ia.108.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dd1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565219
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dz1', '54.e1', '54.m1', '54.y1'], 'contains': ['216.dg1', '216.dj1', '216.do1', '216.gi1', '216.gl1', '216.gu1', '216.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 43908480, 40297548, 36933], 'label': '6912.ia.108.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.de1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565220
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ea1', '54.f1', '54.i1', '54.bb1'], 'contains': ['216.dh1', '216.di1', '216.dk1', '216.gm1', '216.go1', '216.gs1', '216.gx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.108.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.df1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565221
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eb1', '54.e1', '54.j1', '54.bb1'], 'contains': ['216.di1', '216.dj1', '216.dl1', '216.gp1', '216.gt1', '216.gv1', '216.gz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83480268, 83481548, 87305679948], 'label': '6912.ia.108.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565222
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ec1', '54.e1', '54.i1', '54.bc1'], 'contains': ['216.di1', '216.dm1', '216.do1', '216.gr1', '216.he1', '216.hc1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87222200426, 40297548, 87222199680, 36933], 'label': '6912.ia.108.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dh1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565223
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ed1', '36.eg1', '54.f1', '54.n1', '54.y1'], 'contains': ['216.dg1', '216.dk1', '216.dp1', '216.gh1', '216.gw1', '216.hh1', '216.hj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43909226, 32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.108.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.di1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565224
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ee1', '36.eh1', '54.f1', '54.j1', '54.bc1'], 'contains': ['216.di1', '216.dn1', '216.dp1', '216.gq1', '216.hd1', '216.hi1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87222200426, 87222199680, 36933, 87124129, 87109068], 'label': '6912.ia.108.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565225
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.el1', '54.d1', '54.o1', '54.bb1'], 'contains': ['216.ds1', '216.dw1', '216.eb1', '216.el1', '216.em1', '216.go1', '216.gv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87265400268, 83480268, 119769548], 'label': '6912.ia.108.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dk1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565226
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.em1', '54.c1', '54.p1', '54.bb1'], 'contains': ['216.ds1', '216.dx1', '216.ea1', '216.en1', '216.eo1', '216.gx1', '216.gz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.108.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565227
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.en1', '54.c1', '54.o1', '54.bc1'], 'contains': ['216.ds1', '216.dy1', '216.ec1', '216.eq1', '216.er1', '216.hd1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 87222200426, 40297548, 36933], 'label': '6912.ia.108.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565228
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1728.bj1', '1728.cf1', '1728.bg1', '1728.bx1', '1728.bz1', '1728.by1', '1728.ch1', '1728.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.e1', '2.g1'], 'contains': ['8.a1', '12.h1', '12.cw1', '12.cx1', '12.cy1', '16.e1', '16.m1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 47537280, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.e1', '2.g1'], 'normal_contains': ['8.a1', '12.h1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243565229
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.be1'], 'contains': ['24.cy1', '36.ir1', '36.ix1', '48.bz1', '48.eo1'], 'core': '72.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93525427956, 127370880, 40312609, 47537280, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.12.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1', 'old_label': '12.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cy1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565230
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ei1', '36.eo1', '54.d1', '54.p1', '54.bc1'], 'contains': ['216.ds1', '216.dz1', '216.ed1', '216.ep1', '216.es1', '216.hc1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185911680, 32929, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.108.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565231
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ep1', '54.b1', '54.o1', '54.bd1'], 'contains': ['216.du1', '216.dw1', '216.dy1', '216.ew1', '216.ey1', '216.fg1', '216.fh1', '216.lk1', '216.ll1', '216.lo1', '216.lp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 87265400268, 83480268], 'label': '6912.ia.108.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.do1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565232
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eq1', '54.a1', '54.p1', '54.bd1'], 'contains': ['216.du1', '216.dx1', '216.dz1', '216.ez1', '216.fa1', '216.fi1', '216.fj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 36933, 87100665, 87305679948], 'label': '6912.ia.108.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dp1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565233
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.er1', '54.a1', '54.o1', '54.be1'], 'contains': ['216.du1', '216.eb1', '216.ec1', '216.fc1', '216.fd1', '216.fl1', '216.fm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 40297548, 7621226, 36933], 'label': '6912.ia.108.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565234
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ej1', '36.es1', '54.b1', '54.p1', '54.be1'], 'contains': ['216.du1', '216.ea1', '216.ed1', '216.fb1', '216.fe1', '216.fk1', '216.fn1', '216.lj1', '216.lm1', '216.ln1', '216.lq1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185911680, 36933, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.108.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dr1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565235
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.et1', '54.d1', '54.m1', '54.bd1'], 'contains': ['216.dv1', '216.dw1', '216.dz1', '216.fp1', '216.fq1', '216.gn1', '216.gu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 87265400268, 83480268], 'label': '6912.ia.108.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ds1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565236
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eu1', '54.c1', '54.n1', '54.bd1'], 'contains': ['216.dv1', '216.dx1', '216.dy1', '216.fr1', '216.fs1', '216.gw1', '216.gy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 36933, 87100665, 87305679948], 'label': '6912.ia.108.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dt1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565237
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ev1', '54.c1', '54.m1', '54.be1'], 'contains': ['216.dv1', '216.ea1', '216.ec1', '216.fu1', '216.fv1', '216.hb1', '216.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 43909226, 40297548, 36933], 'label': '6912.ia.108.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.du1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565238
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ek1', '36.ew1', '54.d1', '54.n1', '54.be1'], 'contains': ['216.dv1', '216.eb1', '216.ed1', '216.ft1', '216.fw1', '216.ha1', '216.hj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 87109068, 87124129, 32929], 'label': '6912.ia.108.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565239
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ex1', '54.h1', '54.o1', '54.x1'], 'contains': ['216.ej1', '216.el1', '216.eq1', '216.fg1', '216.fl1', '216.gf1', '216.gk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 43945413, 36933, 87100665, 87265400268], 'label': '6912.ia.108.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dw1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565240
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '6.t1', '6.x1', '6.bl1'], 'contains': ['24.b1', '24.u1', '24.z1', '36.jb1', '36.jc1', '48.cb1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.cz1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cz1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243565241
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ey1', '54.g1', '54.p1', '54.x1'], 'contains': ['216.ej1', '216.eo1', '216.ep1', '216.fj1', '216.fk1', '216.gg1', '216.gj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 43945413, 36933, 87100665, 87305679948], 'label': '6912.ia.108.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565242
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ez1', '54.g1', '54.o1', '54.y1'], 'contains': ['216.ej1', '216.em1', '216.er1', '216.fh1', '216.fm1', '216.gh1', '216.gl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 40297548, 7621226, 36933], 'label': '6912.ia.108.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dy1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565243
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fa1', '36.ff1', '54.h1', '54.p1', '54.y1'], 'contains': ['216.ej1', '216.en1', '216.es1', '216.fi1', '216.fn1', '216.gi1', '216.hh1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43908480, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.108.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565244
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fb1', '54.h1', '54.k1', '54.bb1'], 'contains': ['216.ek1', '216.el1', '216.en1', '216.fx1', '216.fz1', '216.gm1', '216.gt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.108.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ea1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565245
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fc1', '54.g1', '54.l1', '54.bb1'], 'contains': ['216.ek1', '216.em1', '216.eo1', '216.fy1', '216.ga1', '216.gp1', '216.gs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83480268, 119769548, 87305679948], 'label': '6912.ia.108.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eb1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565246
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fd1', '54.g1', '54.k1', '54.bc1'], 'contains': ['216.ek1', '216.ep1', '216.er1', '216.gb1', '216.gd1', '216.gq1', '216.he1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 87222199680, 36933, 87185912426], 'label': '6912.ia.108.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ec1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565247
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fe1', '36.fg1', '54.h1', '54.l1', '54.bc1'], 'contains': ['216.ek1', '216.eq1', '216.es1', '216.gc1', '216.ge1', '216.gr1', '216.hi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87222199680, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.108.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ed1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565248
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fh1', '54.f1', '54.o1', '54.z1'], 'contains': ['216.ev1', '216.ew1', '216.fc1', '216.gf1', '216.gh1', '216.go1', '216.hd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.108.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ee1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565249
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fi1', '54.e1', '54.p1', '54.z1'], 'contains': ['216.ev1', '216.fa1', '216.fb1', '216.gg1', '216.gi1', '216.gz1', '216.hc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.108.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ef1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565250
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fj1', '54.e1', '54.o1', '54.ba1'], 'contains': ['216.ev1', '216.ey1', '216.fd1', '216.gk1', '216.gl1', '216.gv1', '216.hg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 87222200426, 40297548, 36933], 'label': '6912.ia.108.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565251
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1', '6.z1', '6.bm1'], 'contains': ['24.cm1', '24.co1', '24.cu1', '36.iy1', '36.jd1', '48.eq1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.12.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.da1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565252
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fk1', '54.f1', '54.k1', '54.bd1'], 'contains': ['216.ew1', '216.ex1', '216.ez1', '216.gm1', '216.gn1', '216.gq1', '216.gw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 36933, 87100665, 87265400268], 'label': '6912.ia.108.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eh1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565253
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fl1', '54.e1', '54.l1', '54.bd1'], 'contains': ['216.ex1', '216.ey1', '216.fa1', '216.gp1', '216.gr1', '216.gu1', '216.gy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 83480268, 87305679948], 'label': '6912.ia.108.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ei1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565254
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fm1', '54.e1', '54.k1', '54.be1'], 'contains': ['216.ex1', '216.fb1', '216.fd1', '216.gt1', '216.he1', '216.ha1', '216.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 40297548, 87222199680, 36933], 'label': '6912.ia.108.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ej1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565255
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fn1', '36.fp1', '36.fr1', '54.f1', '54.p1', '54.ba1'], 'contains': ['216.ev1', '216.ez1', '216.fe1', '216.gj1', '216.gx1', '216.hh1', '216.hk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 43908480, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.108.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ek1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565256
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fo1', '36.fq1', '54.f1', '54.l1', '54.be1'], 'contains': ['216.ex1', '216.fc1', '216.fe1', '216.gs1', '216.hb1', '216.hi1', '216.hj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36933, 43909226, 87222199680, 87109068, 87124129, 32929], 'label': '6912.ia.108.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.el1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565257
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fs1', '54.h1', '54.i1', '54.bd1'], 'contains': ['216.ff1', '216.fg1', '216.fi1', '216.fp1', '216.fr1', '216.gm1', '216.gr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 36933, 87100665, 87265400268], 'label': '6912.ia.108.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.em1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565258
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ft1', '54.g1', '54.j1', '54.bd1'], 'contains': ['216.ff1', '216.fh1', '216.fj1', '216.fq1', '216.fs1', '216.gp1', '216.gq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 83480268, 87305679948], 'label': '6912.ia.108.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.en1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565259
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fu1', '54.g1', '54.i1', '54.be1'], 'contains': ['216.ff1', '216.fk1', '216.fm1', '216.ft1', '216.fv1', '216.gs1', '216.he1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 87222199680, 7621226, 36933], 'label': '6912.ia.108.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eo1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565260
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fv1', '36.fw1', '54.h1', '54.j1', '54.be1'], 'contains': ['216.ff1', '216.fl1', '216.fn1', '216.fu1', '216.fw1', '216.gt1', '216.hi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36933, 87222199680, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.108.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ep1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565261
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fx1', '54.h1', '54.m1', '54.z1'], 'contains': ['216.fo1', '216.fp1', '216.fu1', '216.fx1', '216.gc1', '216.gf1', '216.gi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.108.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565262
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '6.ba1', '6.bm1'], 'contains': ['24.cm1', '24.cp1', '24.cr1', '36.iz1', '36.je1', '48.er1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.12.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.db1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243565263
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fy1', '54.g1', '54.n1', '54.z1'], 'contains': ['216.fo1', '216.fs1', '216.ft1', '216.ga1', '216.gb1', '216.gg1', '216.gh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.108.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.er1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565264
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fz1', '54.g1', '54.m1', '54.ba1'], 'contains': ['216.fo1', '216.fq1', '216.fv1', '216.fy1', '216.gd1', '216.gj1', '216.gl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 40297548, 36933, 87185912426], 'label': '6912.ia.108.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.es1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565265
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ga1', '36.gb1', '36.gc1', '54.h1', '54.n1', '54.ba1'], 'contains': ['216.fo1', '216.fr1', '216.fw1', '216.fz1', '216.ge1', '216.gk1', '216.hh1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 43908480, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.108.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.et1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565266
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gx1', '36.hg1', '54.q1'], 'contains': ['216.bg1', '216.bh1', '216.bk1', '216.bl1', '216.cz1', '216.dc1', '216.ef1', '216.eh1', '216.hs1', '216.ht1', '216.hv1', '216.hx1', '216.hz1', '216.ie1', '216.ih1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 36933, 87305671545, 40279680], 'label': '6912.ia.108.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565267
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gy1', '36.hh1', '54.q1', '54.x1', '54.y1'], 'contains': ['216.bi1', '216.bj1', '216.bm1', '216.dd1', '216.dg1', '216.ej1', '216.hs1', '216.hu1', '216.hy1', '216.ia1', '216.ii1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 36933, 40279680], 'label': '6912.ia.108.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fe1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565268
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gz1', '36.hi1', '54.q1', '54.z1', '54.ba1'], 'contains': ['216.bn1', '216.bo1', '216.bp1', '216.eu1', '216.ev1', '216.fo1', '216.ht1', '216.hu1', '216.if1', '216.ig1', '216.ij1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 87222200426, 36933, 40279680], 'label': '6912.ia.108.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ff1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565269
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ha1', '36.hj1', '54.s1', '54.x1', '54.z1'], 'contains': ['216.bq1', '216.br1', '216.by1', '216.gf1', '216.gg1', '216.hl1', '216.hu1', '216.hv1', '216.ik1', '216.im1', '216.ir1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 36933, 87265400268, 40279680], 'label': '6912.ia.108.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565270
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hb1', '36.hk1', '54.r1', '54.y1', '54.z1'], 'contains': ['216.bs1', '216.bt1', '216.gh1', '216.gi1', '216.hu1', '216.in1', '216.ip1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 36933, 119769548, 40279680], 'label': '6912.ia.108.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565271
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hc1', '36.hl1', '54.r1', '54.x1', '54.ba1'], 'contains': ['216.bu1', '216.bv1', '216.gj1', '216.gk1', '216.hu1', '216.io1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 36933, 87298060748, 40279680], 'label': '6912.ia.108.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565272
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.hd1', '36.he1', '36.hf1', '54.s1', '54.y1', '54.ba1'], 'contains': ['216.a1', '216.bw1', '216.bx1', '216.gl1', '216.hh1', '216.hu1', '216.il1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 36933, 87109068, 40279680], 'label': '6912.ia.108.fj1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fj1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565273
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '6.z1', '6.bn1'], 'contains': ['24.cm1', '24.cq1', '24.cs1', '36.ja1', '36.jf1', '48.es1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.12.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dc1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565274
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hm1', '36.hn1', '54.q1'], 'contains': ['216.cw1', '216.cx1', '216.da1', '216.db1', '216.dq1', '216.dr1', '216.eg1', '216.ei1', '216.hw1', '216.hx1', '216.hy1', '216.ib1', '216.id1', '216.if1', '216.ih1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 36933, 87305671545, 40279680], 'label': '6912.ia.108.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '108.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fk1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565275
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ho1', '36.hp1', '36.hq1', '54.q1', '54.bb1', '54.bc1'], 'contains': ['216.cy1', '216.de1', '216.df1', '216.di1', '216.ds1', '216.ek1', '216.hw1', '216.hz1', '216.ia1', '216.ic1', '216.ij1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 87222200426, 36933, 40279680], 'label': '6912.ia.108.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565276
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hr1', '36.hv1', '54.u1', '54.x1', '54.bb1'], 'contains': ['216.dh1', '216.dl1', '216.el1', '216.eo1', '216.ia1', '216.ik1', '216.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 36933, 87265400268, 40279680], 'label': '6912.ia.108.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565277
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hs1', '36.hw1', '54.t1', '54.y1', '54.bb1'], 'contains': ['216.dk1', '216.dj1', '216.en1', '216.em1', '216.ia1', '216.il1', '216.ip1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.108.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565278
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ht1', '36.hx1', '36.hz1', '54.t1', '54.x1', '54.bc1'], 'contains': ['216.dm1', '216.dn1', '216.ep1', '216.eq1', '216.ia1', '216.im1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87298060748, 87261771468, 40279680], 'label': '6912.ia.108.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fo1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565279
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.hu1', '36.hy1', '36.ia1', '54.u1', '54.y1', '54.bc1'], 'contains': ['216.a1', '216.do1', '216.dp1', '216.er1', '216.es1', '216.ia1', '216.in1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 36933, 87109068, 40279680], 'label': '6912.ia.108.fp1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '108.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565280
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ic1', '36.id1', '54.q1', '54.bd1', '54.be1'], 'contains': ['216.dt1', '216.du1', '216.dv1', '216.et1', '216.ex1', '216.ff1', '216.ib1', '216.ic1', '216.ie1', '216.ig1', '216.ii1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 43909226, 36933, 40279680], 'label': '6912.ia.108.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565281
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ie1', '36.ii1', '54.s1', '54.bb1', '54.bd1'], 'contains': ['216.dw1', '216.dx1', '216.ee1', '216.gm1', '216.gp1', '216.hm1', '216.ic1', '216.id1', '216.ik1', '216.il1', '216.ir1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.108.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fr1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565282
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.if1', '36.ij1', '36.im1', '54.r1', '54.bc1', '54.bd1'], 'contains': ['216.dy1', '216.dz1', '216.gq1', '216.gr1', '216.ic1', '216.in1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 36933, 87298060748, 40279680], 'label': '6912.ia.108.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565283
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ig1', '36.ik1', '54.r1', '54.bb1', '54.be1'], 'contains': ['216.ea1', '216.eb1', '216.gs1', '216.gt1', '216.ic1', '216.io1', '216.ip1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 36933, 119769548, 40279680], 'label': '6912.ia.108.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ft1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565284
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '6.v1', '6.ba1', '6.bn1'], 'contains': ['24.c1', '24.cm1', '24.ct1', '36.jb1', '36.jg1', '48.et1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.dd1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dd1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243565285
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ib1', '36.ih1', '36.il1', '36.in1', '54.s1', '54.bc1', '54.be1'], 'contains': ['216.a1', '216.ec1', '216.ed1', '216.he1', '216.hi1', '216.ic1', '216.im1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 36933, 87109068, 40279680], 'label': '6912.ia.108.fu1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fu1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565286
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.io1', '36.is1', '54.u1', '54.z1', '54.bd1'], 'contains': ['216.ew1', '216.fa1', '216.fp1', '216.fs1', '216.ig1', '216.ik1', '216.in1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 36933, 87265400268, 40279680], 'label': '6912.ia.108.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565287
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ip1', '36.it1', '54.t1', '54.ba1', '54.bd1'], 'contains': ['216.ez1', '216.ey1', '216.fr1', '216.fq1', '216.ig1', '216.il1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87298060748, 83480268, 40279680], 'label': '6912.ia.108.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fw1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565288
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.iq1', '36.iu1', '54.t1', '54.z1', '54.be1'], 'contains': ['216.fb1', '216.fc1', '216.ft1', '216.fu1', '216.ig1', '216.im1', '216.ip1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87261771468, 119769548, 40279680], 'label': '6912.ia.108.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565289
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ir1', '36.iv1', '36.iw1', '36.ix1', '54.u1', '54.ba1', '54.be1'], 'contains': ['216.a1', '216.fd1', '216.fe1', '216.fv1', '216.fw1', '216.ig1', '216.io1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.108.fy1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fy1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565290
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.iy1', '36.jd1', '54.w1', '54.x1', '54.bd1'], 'contains': ['216.fg1', '216.fj1', '216.gn1', '216.gy1', '216.ii1', '216.ik1', '216.iq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 36933, 87265400268, 40279680], 'label': '6912.ia.108.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565291
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.iz1', '36.je1', '54.v1', '54.y1', '54.bd1'], 'contains': ['216.fi1', '216.fh1', '216.gw1', '216.gu1', '216.ii1', '216.il1', '216.in1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 36933, 83480268, 40279680], 'label': '6912.ia.108.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ga1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565292
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ja1', '36.jf1', '54.v1', '54.x1', '54.be1'], 'contains': ['216.fk1', '216.fl1', '216.ha1', '216.hb1', '216.ii1', '216.im1', '216.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 36933, 87261771468, 40279680], 'label': '6912.ia.108.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gb1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565293
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jb1', '36.jc1', '36.jg1', '36.jh1', '54.w1', '54.y1', '54.be1'], 'contains': ['216.a1', '216.fm1', '216.fn1', '216.hf1', '216.hj1', '216.ii1', '216.ip1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 36933, 87109068, 40279680], 'label': '6912.ia.108.gc1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '108.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gc1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565294
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ji1', '36.jn1', '54.w1', '54.z1', '54.bb1'], 'contains': ['216.fx1', '216.ga1', '216.go1', '216.gz1', '216.ij1', '216.ik1', '216.ip1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.108.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gd1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565295
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '6.w1'], 'contains': ['24.cw1', '36.jb1', '36.jh1', '48.cd1', '48.eu1', '48.ev1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 43909226, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.12.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '12.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.de1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 243565296
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jj1', '36.jo1', '54.v1', '54.ba1', '54.bb1'], 'contains': ['216.fz1', '216.fy1', '216.gx1', '216.gv1', '216.ij1', '216.il1', '216.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 36933, 83480268, 40279680], 'label': '6912.ia.108.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ge1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565297
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jk1', '36.jp1', '36.js1', '54.v1', '54.z1', '54.bc1'], 'contains': ['216.gb1', '216.gc1', '216.hc1', '216.hd1', '216.ij1', '216.im1', '216.in1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 36933, 87261771468, 40279680], 'label': '6912.ia.108.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gf1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565298
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jl1', '36.jm1', '36.jq1', '36.jr1', '36.jt1', '36.ju1', '36.jv1', '54.w1', '54.ba1', '54.bc1'], 'contains': ['216.a1', '216.gd1', '216.ge1', '216.hg1', '216.hk1', '216.ij1', '216.iq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.108.gg1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565299
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kf1', '54.b1'], 'contains': ['216.jn1', '216.jp1', '216.jr1', '216.ju1', '216.jt1', '216.kg1', '216.kf1', '216.kj1', '216.kl1', '216.kw1', '216.ky1', '216.lc1', '216.lb1', '216.lo1', '216.ln1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 87124129, 87109068, 87265382400], 'label': '6912.ia.108.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gl1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565300
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kd1', '36.kg1', '54.b1'], 'contains': ['216.jn1', '216.jq1', '216.js1', '216.jv1', '216.jw1', '216.kh1', '216.ki1', '216.kl1', '216.km1', '216.kx1', '216.kz1', '216.ld1', '216.le1', '216.lp1', '216.lq1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 7621226, 36933, 87265382400], 'label': '6912.ia.108.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gm1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565301
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kh1', '54.b1'], 'contains': ['216.jo1', '216.jp1', '216.jq1', '216.jy1', '216.jx1', '216.kc1', '216.kb1', '216.kn1', '216.kp1', '216.kw1', '216.kx1', '216.lg1', '216.lf1', '216.lk1', '216.lj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 83463146, 87124129, 87109068, 87265382400], 'label': '6912.ia.108.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.gn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565302
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '108.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ke1', '36.ki1', '54.b1'], 'contains': ['216.jo1', '216.jr1', '216.js1', '216.jz1', '216.ka1', '216.kd1', '216.ke1', '216.kp1', '216.kq1', '216.ky1', '216.kz1', '216.lh1', '216.li1', '216.ll1', '216.lm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 83463146, 87265382400], 'label': '6912.ia.108.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.go1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565303
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.i1', '64.a1', '64.b1', '64.c1', '64.d1', '64.e1', '64.f1', '64.g1'], 'contains': ['256.a1', '384.a1', '384.b1', '384.c1', '384.d1', '384.e1', '384.f1', '384.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 36933], 'label': '6912.ia.128.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565304
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '64.a1', '64.h1', '64.i1', '64.j1'], 'contains': ['256.a1', '384.i1', '384.j1', '384.k1', '384.l1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 87178328133], 'label': '6912.ia.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.b1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565305
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.l1', '64.b1', '64.h1', '64.l1', '64.m1'], 'contains': ['256.a1', '384.n1', '384.o1', '384.p1', '384.q1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 93405312000, 7657413, 47537280], 'label': '6912.ia.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.c1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565306
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.t1', '6.y1', '6.bh1'], 'contains': ['24.b1', '24.w1', '24.ba1', '36.jl1', '36.jm1', '36.jr1', '48.cf1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.df1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.df1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243565307
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '64.c1', '64.i1', '64.l1', '64.n1'], 'contains': ['256.a1', '384.s1', '384.t1', '384.u1', '384.v1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 36239, 93405312000, 47537280], 'label': '6912.ia.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.d1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565308
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '64.d1', '64.h1', '64.n1', '64.o1'], 'contains': ['256.a1', '384.w1', '384.x1', '384.y1', '384.z1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 87185948613], 'label': '6912.ia.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.e1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565309
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.o1', '64.e1', '64.i1', '64.m1', '64.o1'], 'contains': ['256.a1', '384.bb1', '384.bc1', '384.bd1', '384.be1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 87178327439, 93405312000, 47537280], 'label': '6912.ia.128.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.f1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565310
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '64.f1', '64.j1', '64.l1', '64.o1'], 'contains': ['256.a1', '384.bf1', '384.bg1', '384.bh1', '384.bi1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [43570136, 93405312000, 79833600, 83468087], 'label': '6912.ia.128.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.g1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565311
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '64.g1', '64.j1', '64.m1', '64.n1'], 'contains': ['256.a1', '384.bk1', '384.bl1', '384.bm1', '384.bn1', '384.bo1', '384.bp1', '384.bq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [43570136, 93405312000, 79833600, 87261759287], 'label': '6912.ia.128.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '128.h1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243565312
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.bl1', '48.bm1', '72.ja1', '72.jb1', '72.jc1', '72.jd1', '72.je1'], 'contains': ['288.a1', '288.e1', '288.h1', '288.m1', '288.ir1', '432.eh1'], 'core': '144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.144.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.a1', 'normal_contained_in': ['36.a1', '48.a1'], 'normal_contains': ['288.a1', '288.e1', '576.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565313
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': ['48.gt1', '48.gl1', '48.gn1', '48.go1', '48.gr1', '48.gs1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '48.dc1', '48.dd1', '72.bg1', '72.mp1', '72.ms1', '72.mw1', '72.nb1'], 'contains': ['288.c1', '288.cp1', '288.gf1', '432.fj1'], 'core': '144.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.144.c1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.c1', 'normal_contained_in': ['36.a1', '48.d1'], 'normal_contains': ['288.c1', '576.a1'], 'normalizer': '1.a1', 'old_label': '144.b1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565314
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '48.bo1', '48.bp1', '72.is1', '72.jm1', '72.jn1', '72.jo1', '72.jp1'], 'contains': ['288.b1', '288.f1', '432.ei1', '576.m1'], 'core': '144.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.144.b1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1', 'normal_contained_in': ['36.b1', '48.b1'], 'normal_contains': ['288.b1', '288.f1'], 'normalizer': '1.a1', 'old_label': '144.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565315
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': ['48.gv1', '48.gm1', '48.go1', '48.g1', '48.gc1', '48.gd1'], 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.dy1', '48.dz1', '72.mc1', '72.ee1', '72.np1', '72.ol1', '72.po1'], 'contains': ['288.d1', '432.hp1', '576.s1'], 'core': '144.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 32929, 36933, 746, 2676], 'label': '6912.ia.144.d1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.d1', 'normal_contained_in': ['36.c1', '48.e1'], 'normal_contains': ['288.d1'], 'normalizer': '1.a1', 'old_label': '144.d1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.43', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565316
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '48.h1', '72.d1', '72.e1', '72.ir1'], 'contains': ['288.g1', '288.cb1', '288.j1', '288.p1', '288.cs1', '288.jh1', '288.hq1', '432.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.144.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565317
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1', '6.bb1', '6.bf1'], 'contains': ['24.cn1', '24.co1', '24.ct1', '36.ji1', '36.jn1', '48.ez1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.12.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dg1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565318
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '48.i1', '72.d1', '72.f1', '72.iu1'], 'contains': ['288.g1', '288.ce1', '288.cf1', '288.o1', '288.u1', '288.dm1', '288.dn1', '288.ji1', '288.hr1', '432.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40280426, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.144.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565319
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '48.j1', '72.e1', '72.g1', '72.iu1'], 'contains': ['288.g1', '288.cf1', '288.s1', '288.z1', '288.do1', '288.jj1', '288.hs1', '432.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178291200, 36933, 40310618, 87096887, 40279680], 'label': '6912.ia.144.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565320
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '48.k1', '72.d1', '72.g1', '72.iv1'], 'contains': ['288.g1', '288.cg1', '288.x1', '288.bc1', '288.dp1', '288.jk1', '288.ht1', '432.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.144.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565321
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '48.l1', '72.f1', '72.g1', '72.ir1'], 'contains': ['288.g1', '288.bq1', '288.br1', '288.jl1', '432.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43908480, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.144.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565322
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '48.m1', '72.e1', '72.f1', '72.iv1'], 'contains': ['288.g1', '288.bs1', '288.bt1', '288.jm1', '432.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43909226, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.144.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565323
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gj1', '48.bk1', '48.bl1', '72.ir1', '72.iu1', '72.iv1'], 'contains': ['288.g1', '288.l1', '288.bw1', '288.iq1', '288.jn1', '432.eh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.144.ft1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '144.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ft1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565324
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.bk1', '72.is1', '72.it1', '72.iw1', '72.iy1', '72.iz1'], 'contains': ['288.b1', '288.jo1', '432.eh1', '576.h1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.144.fu1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565325
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.go1', '48.bk1', '48.bm1', '72.ix1'], 'contains': ['288.bz1', '288.jp1', '432.eh1', '576.i1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127370880, 87178291200, 36933, 40279680], 'label': '6912.ia.144.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bd1', 'old_label': '144.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565326
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jw1', '48.cq1', '48.cs1', '72.d1'], 'contains': ['288.cb1', '288.ce1', '288.cg1', '288.cv1', '288.cz1', '288.en1', '288.ep1', '288.jq1', '432.es1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87178291200, 7621226, 36933, 2676], 'label': '6912.ia.144.hg1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '144.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565327
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jx1', '48.ct1', '72.d1'], 'contains': ['288.cb1', '288.cf1', '288.cg1', '288.cx1', '288.dc1', '288.eo1', '288.eq1', '288.jr1', '432.et1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 6851, 87178291200, 36933, 83468087], 'label': '6912.ia.144.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '144.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565328
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '6.bc1', '6.bf1'], 'contains': ['24.cn1', '24.cp1', '24.cs1', '36.jj1', '36.jo1', '48.fa1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.12.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dh1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565329
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ge1', '48.cq1', '48.cu1', '72.lx1'], 'contains': ['288.cc1', '288.cd1', '288.ch1', '288.di1', '288.dj1', '288.dz1', '288.es1', '288.js1', '432.es1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.144.hi1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '144.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565330
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gf1', '48.cv1', '72.lx1', '72.ly1', '72.lz1'], 'contains': ['288.cc1', '288.cj1', '288.ck1', '288.dk1', '288.dl1', '288.ez1', '288.fa1', '432.eu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.144.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565331
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gg1', '48.cw1', '72.lx1'], 'contains': ['288.cd1', '288.ch1', '288.ck1', '288.ef1', '288.ei1', '288.fj1', '288.fk1', '432.ex1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178291200, 47537280, 7621226, 36933, 7629945], 'label': '6912.ia.144.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '144.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565332
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gh1', '48.cx1', '72.lx1', '72.ma1', '72.mb1'], 'contains': ['288.cd1', '288.cj1', '288.ec1', '288.el1', '288.fl1', '432.ey1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.144.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hl1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565333
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gi1', '48.cy1', '72.lx1', '72.mf1', '72.mg1'], 'contains': ['288.ch1', '288.cj1', '288.fv1', '288.fw1', '288.gc1', '432.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 79870533, 36933, 83498639], 'label': '6912.ia.144.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565334
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '48.cr1', '72.h1', '72.lw1', '72.mc1', '72.md1', '72.me1'], 'contains': ['288.d1', '432.fj1', '576.g1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 36933, 2676], 'label': '6912.ia.144.hn1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565335
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gk1', '48.cz1', '72.lz1', '72.ma1', '72.mf1'], 'contains': ['288.cj1', '288.ck1', '288.gz1', '288.ha1', '288.hg1', '432.ff1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [32929, 87178291200, 79833600, 36933, 83480268], 'label': '6912.ia.144.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ho1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565336
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.hp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gl1', '48.da1', '72.ly1', '72.mb1', '72.mf1'], 'contains': ['288.cj1', '288.hb1', '288.hc1', '432.fg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 47537280, 34210, 36933], 'label': '6912.ia.144.hp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565337
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gm1', '48.db1', '72.ly1', '72.ma1', '72.mg1'], 'contains': ['288.cj1', '288.hd1', '288.he1', '432.fi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 7654690, 47537280, 36933], 'label': '6912.ia.144.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565338
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gn1', '48.cr1', '48.dc1', '72.lz1', '72.mb1', '72.mg1'], 'contains': ['288.cj1', '288.gy1', '288.hf1', '432.fj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.144.hr1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '144.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565339
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['1728.bg1', '1728.bx1', '1728.bh1', '1728.bi1', '1728.cd1', '1728.cc1', '1728.ce1', '1728.cg1', '1728.ch1', '1728.cb1', '1728.ca1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.g1'], 'contains': ['8.a1', '12.i1', '12.cz1', '12.dd1', '12.de1', '16.f1', '16.n1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 43909226, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.c1', '2.d1', '2.g1'], 'normal_contains': ['8.a1', '12.i1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243565340
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '6.bb1', '6.bg1'], 'contains': ['24.cn1', '24.cq1', '24.cr1', '36.jk1', '36.jp1', '36.js1', '48.fb1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.12.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.di1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565341
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.go1', '48.cr1', '48.dd1', '72.mh1'], 'contains': ['288.hm1', '432.fj1', '576.i1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 9465, 32929, 87178291200, 36933], 'label': '6912.ia.144.hs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dc1', 'old_label': '144.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565342
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.go1', '48.de1', '72.mi1'], 'contains': ['288.hn1', '432.fm1', '576.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [120116474, 127388748, 87178291200, 36933, 87124129], 'label': '6912.ia.144.ht1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.mi1', 'old_label': '144.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ht1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565343
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '72.i1', '72.j1', '72.k1', '72.l1', '72.ja1'], 'contains': ['288.h1', '288.cl1', '288.i1', '288.q1', '288.ct1', '288.jt1', '288.hu1', '432.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.144.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565344
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '72.i1', '72.m1', '72.n1', '72.o1', '72.p1', '72.q1', '72.jb1'], 'contains': ['288.h1', '288.cm1', '288.cn1', '288.n1', '288.t1', '288.dq1', '288.dr1', '288.ju1', '288.hv1', '432.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.144.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565345
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '72.j1', '72.p1', '72.r1', '72.s1', '72.t1', '72.u1', '72.jb1'], 'contains': ['288.h1', '288.cn1', '288.r1', '288.y1', '288.ds1', '288.jv1', '288.hw1', '432.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 87096887, 40279680], 'label': '6912.ia.144.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565346
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1', '72.i1', '72.m1', '72.r1', '72.s1', '72.v1', '72.w1', '72.jc1'], 'contains': ['288.h1', '288.co1', '288.w1', '288.bb1', '288.dt1', '288.jw1', '288.hx1', '432.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.144.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565347
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.q1', '72.u1', '72.w1', '72.x1', '72.z1', '72.y1', '72.ba1', '72.bb1', '72.bc1', '72.bd1', '72.be1', '72.bf1', '72.bg1', '72.jd1'], 'contains': ['288.h1', '288.cp1', '288.cq1', '288.be1', '288.bh1', '288.du1', '288.dv1', '432.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.144.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565348
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.eg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1', '72.n1', '72.r1', '72.x1', '72.bh1', '72.ja1'], 'contains': ['288.h1', '288.bf1', '288.bi1', '288.jx1', '432.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 43908480, 87178291200, 36933, 87091200], 'label': '6912.ia.144.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565349
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.p1', '72.v1', '72.bf1', '72.bh1', '72.bi1', '72.jd1'], 'contains': ['288.h1', '288.cq1', '288.bg1', '288.bl1', '288.dw1', '432.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.144.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565350
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.o1', '72.s1', '72.x1', '72.z1', '72.bi1', '72.je1'], 'contains': ['288.h1', '288.bk1', '288.bo1', '288.hy1', '432.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.144.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565351
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.v1', '6.bc1', '6.bg1'], 'contains': ['24.c1', '24.cn1', '24.cu1', '36.jl1', '36.jq1', '36.jt1', '48.fc1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.dj1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '12.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dj1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243565352
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.m1', '72.t1', '72.y1', '72.bh1', '72.bi1', '72.je1'], 'contains': ['288.h1', '288.cr1', '288.bj1', '288.bn1', '288.dx1', '432.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7653409, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.144.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565353
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1', '72.j1', '72.n1', '72.o1', '72.t1', '72.v1', '72.ba1', '72.jc1'], 'contains': ['288.h1', '288.bm1', '288.bp1', '288.jy1', '432.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.144.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565354
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cs1', '48.cu1', '72.i1', '72.mj1', '72.mk1'], 'contains': ['288.cl1', '288.cm1', '288.co1', '288.cu1', '288.cy1', '288.dy1', '288.et1', '288.jz1', '432.es1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 7621226, 36933], 'label': '6912.ia.144.hu1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565355
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ct1', '72.i1', '72.mj1', '72.ml1'], 'contains': ['288.cl1', '288.cn1', '288.co1', '288.cw1', '288.db1', '288.er1', '288.eu1', '288.ka1', '432.et1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 83468087], 'label': '6912.ia.144.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565356
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cv1', '72.k1', '72.mk1', '72.ml1', '72.mm1', '72.mn1', '72.mo1', '72.mp1'], 'contains': ['288.cl1', '288.cp1', '288.cr1', '288.de1', '288.dg1', '288.ev1', '288.ex1', '432.eu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.144.hw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565357
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.mj1', '72.mm1'], 'contains': ['288.cl1', '288.cq1', '288.cr1', '288.df1', '288.dh1', '288.ew1', '288.ey1', '432.ev1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.144.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565358
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.q1', '72.mj1'], 'contains': ['288.cm1', '288.cn1', '288.cq1', '288.eb1', '288.eg1', '288.fc1', '288.fn1', '432.ew1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36239, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.144.hy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565359
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cw1', '72.m1', '72.mj1', '72.mk1'], 'contains': ['288.cm1', '288.co1', '288.cr1', '288.ee1', '288.eh1', '288.fm1', '288.fo1', '432.ex1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87178291200, 7621226, 36933, 7629945], 'label': '6912.ia.144.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565360
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cx1', '72.q1', '72.mk1', '72.mq1', '72.mr1', '72.ms1'], 'contains': ['288.cm1', '288.cp1', '288.ed1', '288.ek1', '288.fp1', '432.ey1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 746], 'label': '6912.ia.144.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ia1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565361
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.mj1', '72.ml1'], 'contains': ['288.cn1', '288.co1', '288.cr1', '288.fd1', '288.fg1', '288.fq1', '288.fx1', '432.ez1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 7629945, 83468087], 'label': '6912.ia.144.ib1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ib1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565362
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.w1'], 'contains': ['24.cw1', '36.jl1', '36.ju1', '36.jv1', '48.ch1', '48.fd1', '48.fe1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 93405312000, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.12.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '12.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dk1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
  • id: 243565363
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.u1', '72.ml1', '72.mt1', '72.mu1', '72.mv1', '72.mw1'], 'contains': ['288.cn1', '288.cp1', '288.fe1', '288.fh1', '288.fy1', '432.fa1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 87178291200, 36933], 'label': '6912.ia.144.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ic1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565364
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.u1', '72.mx1'], 'contains': ['288.cn1', '288.cq1', '288.ff1', '288.fi1', '288.fz1', '432.fb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 87178291200, 36933, 87100665], 'label': '6912.ia.144.id1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bm1', 'old_label': '144.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.id1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565365
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cy1', '72.w1', '72.mk1', '72.ml1', '72.my1', '72.mz1', '72.na1', '72.nb1'], 'contains': ['288.co1', '288.cp1', '288.fr1', '288.ft1', '288.ga1', '432.fc1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 83498639], 'label': '6912.ia.144.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ie1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565366
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.mj1', '72.nc1'], 'contains': ['288.co1', '288.cq1', '288.fs1', '288.fu1', '288.gb1', '432.fd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7656719, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.144.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.if1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565367
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '72.bg1', '72.mm1', '72.mq1', '72.mt1', '72.mu1', '72.my1'], 'contains': ['288.cp1', '288.cq1', '288.ge1', '288.gh1', '288.gp1', '432.fe1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 87100665, 87124129], 'label': '6912.ia.144.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ig1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565368
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cz1', '72.y1', '72.mm1', '72.mp1', '72.mr1', '72.mv1', '72.mz1', '72.na1'], 'contains': ['288.cp1', '288.cr1', '288.gg1', '288.gi1', '288.gw1', '432.ff1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 36933, 83480268], 'label': '6912.ia.144.ih1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ih1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565369
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.da1', '72.bb1', '72.mn1', '72.ms1', '72.mt1', '72.mz1'], 'contains': ['288.cp1', '288.gj1', '288.gl1', '432.fg1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 34210, 36933], 'label': '6912.ia.144.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ii1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565370
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.bc1', '72.mo1', '72.mq1', '72.mu1', '72.mw1', '72.na1'], 'contains': ['288.cp1', '288.gk1', '288.gn1', '432.fh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 40313890, 36933], 'label': '6912.ia.144.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ij1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565371
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.db1', '72.bd1', '72.mn1', '72.mo1', '72.mr1', '72.mv1', '72.my1', '72.nb1'], 'contains': ['288.cp1', '288.gm1', '288.go1', '432.fi1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 7654690, 36933], 'label': '6912.ia.144.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ik1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565372
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.mm1', '72.mx1'], 'contains': ['288.cq1', '288.cr1', '288.gq1', '288.gs1', '288.gx1', '432.fk1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7653409, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.144.il1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '144.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.il1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565373
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.n1', '6.bd1', '6.bi1'], 'contains': ['24.d1', '36.jm1', '36.jq1', '36.ju1', '48.ci1', '48.ff1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.dl1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dl1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565374
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '72.mx1', '72.nc1'], 'contains': ['288.cq1', '288.gt1', '288.gu1', '432.fl1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 43942690, 36933, 87100665], 'label': '6912.ia.144.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.im1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565375
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.de1', '72.bf1', '72.nc1'], 'contains': ['288.cq1', '288.gr1', '288.gv1', '432.fm1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127388748, 93405312000, 87178291200, 36933, 87124129], 'label': '6912.ia.144.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '144.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.in1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565376
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1', '48.n1', '72.ir1', '72.bj1', '72.bk1'], 'contains': ['288.j1', '288.l1', '288.br1', '288.kb1', '432.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87218570880, 36933, 2676, 87091200], 'label': '6912.ia.144.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565377
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1', '72.ja1', '72.bl1', '72.bm1', '72.bn1', '72.bo1'], 'contains': ['288.i1', '288.m1', '288.bi1', '288.kc1', '432.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 36933, 87091200], 'label': '6912.ia.144.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565378
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '72.i1', '72.bl1', '72.bp1', '72.bq1', '72.br1', '72.bs1', '72.jf1'], 'contains': ['288.i1', '288.n1', '288.w1', '288.cu1', '288.cw1', '288.kd1', '288.hz1', '432.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.144.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565379
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bz1', '48.o1', '72.d1', '72.bj1', '72.jg1'], 'contains': ['288.j1', '288.o1', '288.x1', '288.cv1', '288.cx1', '288.ke1', '288.ia1', '432.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.144.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565380
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.j1', '72.bm1', '72.br1', '72.bt1', '72.bu1', '72.bv1', '72.jf1'], 'contains': ['288.i1', '288.r1', '288.bm1', '288.kf1', '432.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565381
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ce1', '48.p1', '72.e1', '72.bk1', '72.jg1'], 'contains': ['288.j1', '288.s1', '288.bs1', '288.kg1', '432.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 43909226, 36933, 2676, 87091200], 'label': '6912.ia.144.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565382
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1', '72.i1', '72.bm1', '72.bp1', '72.bt1', '72.bw1', '72.bx1', '72.jh1'], 'contains': ['288.i1', '288.t1', '288.bb1', '288.cy1', '288.db1', '288.kh1', '288.ib1', '432.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87261759287, 87091200], 'label': '6912.ia.144.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565383
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cj1', '48.q1', '72.d1', '72.bk1', '72.ji1'], 'contains': ['288.j1', '288.u1', '288.bc1', '288.cz1', '288.dc1', '288.ki1', '288.ic1', '432.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.144.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565384
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.bj1'], 'contains': ['24.cx1', '36.jm1', '36.jt1', '36.jv1', '48.cj1', '48.fg1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40312609, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.12.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '12.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dm1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565385
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ck1', '48.q1', '72.jj1'], 'contains': ['288.k1', '288.v1', '288.bd1', '288.da1', '288.dd1', '288.kj1', '288.id1', '432.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 93405342938, 36933, 87261759287, 87091200], 'label': '6912.ia.144.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565386
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.j1', '72.bl1', '72.bq1', '72.bu1', '72.bw1', '72.by1', '72.jh1'], 'contains': ['288.i1', '288.y1', '288.bp1', '288.kk1', '432.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.144.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565387
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cp1', '48.r1', '72.e1', '72.bj1', '72.ji1'], 'contains': ['288.j1', '288.z1', '288.bt1', '288.kl1', '432.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.144.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565388
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cq1', '48.r1', '72.jj1'], 'contains': ['288.k1', '288.ba1', '288.bv1', '288.km1', '432.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87222200426, 36933, 93405314676, 87091200], 'label': '6912.ia.144.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565389
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.bn1', '72.bs1', '72.bv1', '72.bx1', '72.by1', '72.bz1', '72.ca1', '72.cb1', '72.cc1', '72.cd1', '72.ce1', '72.cf1', '72.cg1', '72.jk1'], 'contains': ['288.i1', '288.be1', '288.bj1', '288.de1', '288.df1', '432.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87124129], 'label': '6912.ia.144.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565390
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.bo1', '72.bp1', '72.bu1', '72.bz1', '72.ch1', '72.jl1'], 'contains': ['288.i1', '288.bh1', '288.bn1', '288.dg1', '288.dh1', '432.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 87178324129, 36933, 87091200], 'label': '6912.ia.144.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565391
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.bo1', '72.br1', '72.bw1', '72.cf1', '72.ch1', '72.jk1'], 'contains': ['288.i1', '288.bg1', '288.bk1', '432.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 93405312000, 40297548, 36933], 'label': '6912.ia.144.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565392
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.bn1', '72.bq1', '72.bt1', '72.ca1', '72.ch1', '72.jl1'], 'contains': ['288.i1', '288.bl1', '288.bo1', '432.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218603809, 93405312000, 36933, 87091200], 'label': '6912.ia.144.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565393
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1', '48.s1', '72.iu1', '72.bj1', '72.ck1'], 'contains': ['288.l1', '288.o1', '288.z1', '288.dm1', '288.do1', '288.kn1', '288.ie1', '432.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87305662080, 40280426, 36933, 2676, 40279680], 'label': '6912.ia.144.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565394
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1', '48.t1', '72.ir1', '72.ck1', '72.cl1'], 'contains': ['288.l1', '288.p1', '288.bq1', '288.ko1', '432.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.144.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565395
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.be1'], 'contains': ['24.cy1', '36.jq1', '36.jr1', '36.jv1', '48.ck1', '48.fh1'], 'core': '72.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93525427956, 127370880, 40312609, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1', 'old_label': '12.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dn1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565396
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ct1', '48.u1', '72.iu1', '72.bk1', '72.cl1'], 'contains': ['288.l1', '288.s1', '288.u1', '288.dn1', '288.do1', '288.kp1', '288.if1', '432.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87305662080, 36933, 40310618, 87096887, 40279680], 'label': '6912.ia.144.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565397
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '48.v1', '72.iv1', '72.bj1', '72.cl1'], 'contains': ['288.l1', '288.x1', '288.bt1', '288.kq1', '432.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.144.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565398
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '48.w1', '72.iv1', '72.bk1', '72.ck1'], 'contains': ['288.l1', '288.bc1', '288.bs1', '288.kr1', '432.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 43909226, 36933, 2676, 87091200], 'label': '6912.ia.144.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565399
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '72.jb1', '72.bl1', '72.cn1', '72.co1', '72.cp1', '72.cq1', '72.cr1'], 'contains': ['288.m1', '288.n1', '288.y1', '288.dq1', '288.ds1', '288.ks1', '288.ig1', '432.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87305662080, 93405312000, 40280426, 36933, 40279680], 'label': '6912.ia.144.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565400
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1', '72.ja1', '72.cn1', '72.cs1', '72.ct1', '72.cu1'], 'contains': ['288.m1', '288.q1', '288.bf1', '288.kt1', '432.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87218570880, 93405312000, 43908480, 36933, 87091200], 'label': '6912.ia.144.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565401
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.jb1', '72.bm1', '72.cq1', '72.cs1', '72.cv1', '72.cw1', '72.cx1'], 'contains': ['288.m1', '288.r1', '288.t1', '288.dr1', '288.ds1', '288.ku1', '288.ih1', '432.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87305662080, 93405312000, 36933, 87096887, 40279680], 'label': '6912.ia.144.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565402
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1', '72.jc1', '72.bl1', '72.co1', '72.cs1', '72.cv1', '72.cy1', '72.cz1'], 'contains': ['288.m1', '288.w1', '288.bp1', '288.kv1', '432.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.144.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565403
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '72.jc1', '72.bm1', '72.cn1', '72.cp1', '72.cw1', '72.cy1', '72.da1'], 'contains': ['288.m1', '288.bb1', '288.bm1', '288.kw1', '432.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565404
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jd1', '72.bn1', '72.cr1', '72.ct1', '72.cx1', '72.cz1', '72.da1', '72.dh1', '72.dc1', '72.db1', '72.dd1', '72.de1', '72.df1', '72.dg1', '72.di1'], 'contains': ['288.m1', '288.be1', '288.bl1', '288.du1', '288.dw1', '432.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87218570880, 93405312000, 32929, 36933], 'label': '6912.ia.144.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565667
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.in1', '48.ec1', '48.eh1', '72.pn1'], 'contains': ['288.fb1', '288.hi1', '288.hl1', '432.id1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 93452849280, 36933], 'label': '6912.ia.144.mi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '144.mi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565405
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jd1', '72.bo1', '72.cq1', '72.cu1', '72.cy1', '72.dh1', '72.dj1'], 'contains': ['288.m1', '288.bh1', '288.bg1', '288.dv1', '288.dw1', '432.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87218607813, 93405312000, 36933, 87100665], 'label': '6912.ia.144.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565406
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1'], 'contains': ['24.cz1', '36.jr1', '36.jt1', '36.ju1', '36.jv1', '48.cl1', '48.fi1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87222200426, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.12.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.do1', 'old_label': '12.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.do1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 243565407
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.je1', '72.bo1', '72.cp1', '72.ct1', '72.cv1', '72.dc1', '72.dj1'], 'contains': ['288.m1', '288.bk1', '288.bn1', '432.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [119768268, 87218570880, 93405312000, 36933, 87091200], 'label': '6912.ia.144.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565408
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.je1', '72.bn1', '72.co1', '72.cu1', '72.cw1', '72.db1', '72.dj1'], 'contains': ['288.m1', '288.bj1', '288.bo1', '432.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 87091200, 83480268], 'label': '6912.ia.144.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565409
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1', '72.i1', '72.cn1', '72.dk1', '72.dl1', '72.dm1', '72.dt1', '72.jq1'], 'contains': ['288.n1', '288.q1', '288.bb1', '288.dy1', '288.er1', '288.kx1', '288.ii1', '432.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87261759287, 87091200], 'label': '6912.ia.144.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565410
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.bp1', '72.cq1', '72.dk1', '72.dn1', '72.do1', '72.ju1'], 'contains': ['288.n1', '288.t1', '288.bh1', '288.ed1', '288.eg1', '288.fc1', '288.fe1', '432.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87178300665, 40279680], 'label': '6912.ia.144.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565411
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.bs1', '72.co1', '72.dk1', '72.dp1', '72.dr1', '72.jv1'], 'contains': ['288.n1', '288.w1', '288.bj1', '288.ee1', '288.fd1', '432.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.144.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565412
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.bq1', '72.cr1', '72.dl1', '72.dp1', '72.dq1', '72.ju1'], 'contains': ['288.n1', '288.y1', '288.bl1', '288.eg1', '288.ff1', '432.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87305671545, 40279680], 'label': '6912.ia.144.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565413
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.bp1', '72.cp1', '72.dq1', '72.ds1', '72.dt1', '72.jx1'], 'contains': ['288.n1', '288.bb1', '288.bn1', '288.eh1', '288.fg1', '432.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87261763065, 87261759287, 87091200], 'label': '6912.ia.144.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565414
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '72.n1', '72.cn1', '72.dn1', '72.dq1', '72.dr1', '72.du1', '72.jf1'], 'contains': ['288.n1', '288.bf1', '288.bm1', '288.ky1', '432.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 36933, 87091200], 'label': '6912.ia.144.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565415
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1', '72.n1', '72.bl1', '72.do1', '72.dp1', '72.ds1', '72.dw1', '72.jq1'], 'contains': ['288.n1', '288.bi1', '288.bp1', '288.kz1', '432.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222200426, 87222199680, 36933, 87091200], 'label': '6912.ia.144.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565416
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.br1', '72.cp1', '72.dl1', '72.do1', '72.du1', '72.jv1'], 'contains': ['288.n1', '288.bk1', '288.bm1', '432.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565417
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1'], 'contains': ['24.dp1', '24.dq1', '24.dt1', '24.eb1', '24.ee1', '24.eh1', '24.en1', '36.kd1', '36.kg1', '48.df1'], 'core': '48.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36933, 87265382400, 2676, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.12.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565418
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.bq1', '72.co1', '72.dm1', '72.dn1', '72.dw1', '72.jx1'], 'contains': ['288.n1', '288.bo1', '288.bp1', '432.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.144.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565419
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.br1', '72.cq1', '72.dm1', '72.dr1', '72.ds1', '72.ka1'], 'contains': ['288.n1', '288.r1', '288.bg1', '288.eb1', '288.fi1', '432.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 36933, 87100665], 'label': '6912.ia.144.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565420
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.bs1', '72.cr1', '72.dt1', '72.du1', '72.dv1', '72.dw1', '72.dy1', '72.dx1', '72.dz1', '72.ea1', '72.eb1', '72.ec1', '72.ed1', '72.ka1'], 'contains': ['288.n1', '288.be1', '288.eb1', '288.ek1', '288.fh1', '432.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 36933, 40279680], 'label': '6912.ia.144.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565421
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ef1', '48.x1', '72.d1', '72.ck1', '72.kd1'], 'contains': ['288.o1', '288.p1', '288.bc1', '288.en1', '288.eo1', '288.la1', '288.ij1', '432.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.144.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565422
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eg1', '48.y1', '72.f1', '72.ck1', '72.jg1'], 'contains': ['288.o1', '288.bq1', '288.bs1', '288.lb1', '432.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.144.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565423
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.eh1', '48.z1', '72.f1', '72.bj1', '72.kd1'], 'contains': ['288.o1', '288.br1', '288.bt1', '288.lc1', '432.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87222200426, 87222199680, 36933, 2676, 87091200], 'label': '6912.ia.144.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565424
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ei1', '48.ba1', '72.e1', '72.cl1', '72.kd1'], 'contains': ['288.p1', '288.s1', '288.bt1', '288.ld1', '432.bn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.144.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565425
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ej1', '48.bb1', '72.d1', '72.cl1', '72.ke1'], 'contains': ['288.p1', '288.u1', '288.x1', '288.ep1', '288.eq1', '288.le1', '288.ik1', '432.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.144.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565426
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ek1', '48.bc1', '72.e1', '72.ck1', '72.ke1'], 'contains': ['288.p1', '288.z1', '288.bs1', '288.lf1', '432.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 43909226, 36933, 2676, 87091200], 'label': '6912.ia.144.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.co1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565427
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1', '72.j1', '72.cs1', '72.dm1', '72.eg1', '72.eh1', '72.ei1', '72.jq1'], 'contains': ['288.q1', '288.r1', '288.bp1', '288.lg1', '432.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.144.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565428
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1'], 'contains': ['24.dp1', '24.dr1', '24.ds1', '24.ec1', '24.ee1', '24.ek1', '24.em1', '36.ke1', '36.ki1', '48.dg1'], 'core': '48.f1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 2676, 83463146, 87265382400], 'label': '6912.ia.12.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.du1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565429
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1', '72.i1', '72.cs1', '72.dk1', '72.eg1', '72.ej1', '72.ek1', '72.kg1'], 'contains': ['288.q1', '288.t1', '288.w1', '288.et1', '288.eu1', '288.lh1', '288.il1', '432.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.144.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565430
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1', '72.j1', '72.cn1', '72.dl1', '72.eh1', '72.ej1', '72.el1', '72.kg1'], 'contains': ['288.q1', '288.y1', '288.bm1', '288.li1', '432.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565431
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.ct1', '72.dt1', '72.ei1', '72.ek1', '72.el1', '72.em1', '72.en1', '72.eo1', '72.ep1', '72.eq1', '72.er1', '72.es1', '72.et1', '72.kh1'], 'contains': ['288.q1', '288.be1', '288.bn1', '288.ev1', '288.ew1', '432.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 93405312000, 32929, 36933, 87124129], 'label': '6912.ia.144.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565432
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.cu1', '72.dk1', '72.eh1', '72.em1', '72.eu1', '72.ki1'], 'contains': ['288.q1', '288.bh1', '288.bj1', '288.ex1', '288.ey1', '432.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7653409, 93405312000, 87178324129, 36933, 87091200], 'label': '6912.ia.144.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565433
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.cu1', '72.dm1', '72.ej1', '72.es1', '72.eu1', '72.kh1'], 'contains': ['288.q1', '288.bg1', '288.bo1', '432.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87185911680, 93405312000, 40297548, 36933], 'label': '6912.ia.144.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565434
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.ct1', '72.dl1', '72.eg1', '72.en1', '72.eu1', '72.ki1'], 'contains': ['288.q1', '288.bk1', '288.bl1', '432.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 87218603809, 93405312000, 36933, 87091200], 'label': '6912.ia.144.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565435
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.bt1', '72.cx1', '72.eg1', '72.ev1', '72.ew1', '72.ju1'], 'contains': ['288.r1', '288.t1', '288.bl1', '288.fc1', '288.ff1', '432.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87096887, 87305671545, 40279680], 'label': '6912.ia.144.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565436
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1', '72.r1', '72.cs1', '72.dr1', '72.ev1', '72.ex1', '72.ez1', '72.jf1'], 'contains': ['288.r1', '288.w1', '288.bf1', '288.lj1', '432.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 36933, 87091200, 83468087], 'label': '6912.ia.144.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cx1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565437
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '72.br1', '72.cv1', '72.eg1', '72.ey1', '72.ez1', '72.jv1'], 'contains': ['288.r1', '288.w1', '288.bk1', '288.im1', '432.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.144.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243565438
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.bu1', '72.cq1', '72.eh1', '72.ex1', '72.ey1', '72.ju1'], 'contains': ['288.r1', '288.y1', '288.bh1', '288.fe1', '288.ff1', '432.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87096887, 87178300665, 40279680], 'label': '6912.ia.144.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565439
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '32.j1', '48.a1', '48.bk1', '48.bl1', '48.bm1', '64.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.16.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565440
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1', '72.r1', '72.bm1', '72.ds1', '72.ew1', '72.ey1', '72.fa1', '72.jq1'], 'contains': ['288.r1', '288.bb1', '288.bi1', '288.lk1', '432.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222199680, 36933, 87261759287, 87091200], 'label': '6912.ia.144.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.da1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565747
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ju1', '48.fd1', '48.ff1', '48.fi1', '72.mh1'], 'contains': ['288.hm1', '432.jw1', '576.bp1'], 'core': '864.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [120116474, 9465, 32929, 36933, 87185912426], 'label': '6912.ia.144.pb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.mh1', 'old_label': '144.pb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565441
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '72.bt1', '72.cw1', '72.dm1', '72.ex1', '72.fa1', '72.jx1'], 'contains': ['288.r1', '288.bb1', '288.bo1', '288.in1', '432.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 93405312000, 36933, 87261759287, 87091200], 'label': '6912.ia.144.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565442
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '72.bv1', '72.cw1', '72.dr1', '72.eh1', '72.ew1', '72.jv1'], 'contains': ['288.r1', '288.bj1', '288.bm1', '432.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 83471865, 87091200], 'label': '6912.ia.144.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243565443
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '72.bu1', '72.cv1', '72.ds1', '72.ei1', '72.ev1', '72.jx1'], 'contains': ['288.r1', '288.bn1', '288.bp1', '432.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222200426, 36933, 87261763065, 87091200], 'label': '6912.ia.144.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565444
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.bv1', '72.cx1', '72.ei1', '72.ez1', '72.fa1', '72.fb1', '72.fd1', '72.fc1', '72.fe1', '72.ff1', '72.fg1', '72.fh1', '72.fi1', '72.ka1'], 'contains': ['288.r1', '288.be1', '288.fh1', '288.fi1', '432.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87127439, 40279680], 'label': '6912.ia.144.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.de1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565445
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ff1', '48.bd1', '72.g1', '72.cl1', '72.jg1'], 'contains': ['288.s1', '288.x1', '288.bq1', '288.ll1', '432.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43908480, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.144.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.df1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565446
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fg1', '48.be1', '72.g1', '72.bk1', '72.kd1'], 'contains': ['288.s1', '288.bc1', '288.br1', '288.lm1', '432.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [30938, 87222199680, 36933, 87261759287, 87091200], 'label': '6912.ia.144.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565447
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.bp1', '72.cv1', '72.ek1', '72.ev1', '72.fk1', '72.kp1'], 'contains': ['288.t1', '288.w1', '288.bn1', '288.fm1', '288.fq1', '432.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87261763065, 87091200, 83468087], 'label': '6912.ia.144.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565448
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.bx1', '72.cw1', '72.dk1', '72.ew1', '72.fl1', '72.kq1'], 'contains': ['288.t1', '288.bb1', '288.bj1', '288.fo1', '288.fx1', '432.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83471865, 87261759287, 87091200], 'label': '6912.ia.144.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.di1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565449
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1', '72.n1', '72.cs1', '72.dn1', '72.ev1', '72.fl1', '72.fm1', '72.jh1'], 'contains': ['288.t1', '288.bf1', '288.bp1', '288.ln1', '432.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 87222200426, 36933, 87091200], 'label': '6912.ia.144.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565450
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1728.bx1', '1728.bg1', '1728.bh1', '1728.cd1', '1728.cc1', '1728.bi1', '1728.ce1', '1728.cj1', '1728.ci1', '1728.bz1', '1728.by1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.e1', '2.f1'], 'contains': ['8.a1', '12.df1', '12.dj1', '12.dk1', '12.dl1', '12.dm1', '12.dn1', '12.do1', '16.g1', '16.o1'], 'core': '4.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.c1', '2.e1', '2.f1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243565451
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '4.i1'], 'contains': ['32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1', '32.h1', '32.k1', '48.cq1', '48.cs1', '48.cu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.16.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '16.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243565452
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1', '72.n1', '72.bm1', '72.do1', '72.ew1', '72.fk1', '72.fo1', '72.kg1'], 'contains': ['288.t1', '288.bi1', '288.bm1', '288.lo1', '432.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 87222199680, 36933, 87091200], 'label': '6912.ia.144.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565453
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.bw1', '72.cv1', '72.do1', '72.eg1', '72.fm1', '72.kq1'], 'contains': ['288.t1', '288.bk1', '288.bp1', '432.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.144.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565454
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '72.bt1', '72.cw1', '72.dn1', '72.ej1', '72.fo1', '72.kp1'], 'contains': ['288.t1', '288.bm1', '288.bo1', '432.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565455
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fp1', '48.bf1', '72.f1', '72.cl1', '72.ji1'], 'contains': ['288.u1', '288.bq1', '288.bt1', '288.lp1', '432.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43908480, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.144.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565456
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fq1', '48.bg1', '72.f1', '72.bk1', '72.ke1'], 'contains': ['288.u1', '288.br1', '288.bs1', '288.lq1', '432.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43909226, 87222199680, 36933, 2676, 87091200], 'label': '6912.ia.144.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565457
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fr1', '48.bf1', '72.jj1'], 'contains': ['288.v1', '288.bu1', '288.bv1', '288.lr1', '432.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43908480, 87222200426, 36933, 93405314676, 87091200], 'label': '6912.ia.144.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565458
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.bw1', '72.cq1', '72.ej1', '72.fk1', '72.fl1', '72.kr1'], 'contains': ['288.t1', '288.y1', '288.bg1', '288.fn1', '288.fz1', '432.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 93405312000, 87218571626, 36933, 87100665], 'label': '6912.ia.144.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565459
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.bx1', '72.cx1', '72.ek1', '72.fm1', '72.fn1', '72.fo1', '72.fq1', '72.fp1', '72.fr1', '72.fs1', '72.ft1', '72.fu1', '72.fv1', '72.kr1'], 'contains': ['288.t1', '288.be1', '288.fn1', '288.fp1', '288.fy1', '432.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87218571626, 36933, 40279680], 'label': '6912.ia.144.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565460
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1', '72.r1', '72.bl1', '72.dp1', '72.ey1', '72.fk1', '72.fy1', '72.kg1'], 'contains': ['288.w1', '288.y1', '288.bi1', '288.ls1', '432.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222199680, 36933, 87091200, 83468087], 'label': '6912.ia.144.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ds1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565461
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '72.bq1', '72.co1', '72.ej1', '72.ex1', '72.fy1', '72.kp1'], 'contains': ['288.w1', '288.y1', '288.bo1', '288.io1', '432.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87298051065, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.144.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565462
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.i1', '8.j1', '8.k1'], 'contains': ['32.i1', '48.d1', '48.cr1', '48.dc1', '48.dd1', '64.a1'], 'core': '48.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.16.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565463
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.bp1', '72.cy1', '72.dk1', '72.ex1', '72.ey1', '72.ks1'], 'contains': ['288.w1', '288.bb1', '288.bh1', '288.fr1', '288.fs1', '432.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.144.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565464
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '72.br1', '72.cy1', '72.dr1', '72.ej1', '72.fk1', '72.kt1'], 'contains': ['288.w1', '288.bg1', '288.bm1', '432.co1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.144.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243565465
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '72.bq1', '72.cz1', '72.dp1', '72.eg1', '72.ev1', '72.ks1'], 'contains': ['288.w1', '288.bl1', '288.bp1', '432.cp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.144.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565466
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.bs1', '72.cz1', '72.ek1', '72.ez1', '72.fy1', '72.fz1', '72.gb1', '72.ga1', '72.gc1', '72.gd1', '72.ge1', '72.gf1', '72.gg1', '72.kt1'], 'contains': ['288.w1', '288.be1', '288.ft1', '288.fu1', '432.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665], 'label': '6912.ia.144.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565467
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.fw1', '48.bh1', '72.g1', '72.bj1', '72.ke1'], 'contains': ['288.x1', '288.z1', '288.br1', '288.lt1', '432.cl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [30938, 87222199680, 36933, 87091200, 83468087], 'label': '6912.ia.144.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565468
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1', '72.r1', '72.cn1', '72.dq1', '72.ex1', '72.fl1', '72.gi1', '72.jh1'], 'contains': ['288.y1', '288.bb1', '288.bf1', '288.lu1', '432.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 36933, 87261759287, 87091200], 'label': '6912.ia.144.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565469
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '72.bw1', '72.cp1', '72.dl1', '72.ey1', '72.gi1', '72.kq1'], 'contains': ['288.y1', '288.bb1', '288.bk1', '288.ip1', '432.cs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 36933, 87261759287, 87091200], 'label': '6912.ia.144.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565470
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gb1', '48.bi1', '72.g1', '72.ck1', '72.ji1'], 'contains': ['288.z1', '288.bc1', '288.bq1', '288.lv1', '432.cr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43908480, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.144.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565471
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gc1', '48.bi1', '72.jj1'], 'contains': ['288.ba1', '288.bd1', '288.bu1', '288.lw1', '432.cr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405342938, 43908480, 36933, 87261759287, 87091200], 'label': '6912.ia.144.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565472
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '72.by1', '72.co1', '72.dp1', '72.eh1', '72.fl1', '72.kq1'], 'contains': ['288.y1', '288.bj1', '288.bp1', '432.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222200426, 36933, 83471865, 87091200], 'label': '6912.ia.144.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565473
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '8.b1', '8.e1', '8.f1'], 'contains': ['32.a1', '32.l1', '48.b1', '48.bn1', '48.bo1', '48.bp1', '64.b1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.16.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565474
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '72.bu1', '72.cp1', '72.dq1', '72.el1', '72.fk1', '72.kp1'], 'contains': ['288.y1', '288.bm1', '288.bn1', '432.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 87261763065, 87091200], 'label': '6912.ia.144.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565475
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.by1', '72.cr1', '72.el1', '72.fy1', '72.gi1', '72.gj1', '72.gl1', '72.gk1', '72.gm1', '72.gn1', '72.go1', '72.gp1', '72.gq1', '72.kr1'], 'contains': ['288.y1', '288.be1', '288.fy1', '288.fz1', '432.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87265418639, 40279680], 'label': '6912.ia.144.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ef1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565476
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '72.bw1', '72.cy1', '72.dm1', '72.ds1', '72.fl1', '72.kw1'], 'contains': ['288.bb1', '288.bg1', '288.bp1', '432.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.144.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565477
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '72.bt1', '72.da1', '72.dl1', '72.dq1', '72.ew1', '72.ks1'], 'contains': ['288.bb1', '288.bl1', '288.bm1', '432.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 87091200, 87305671545], 'label': '6912.ia.144.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eh1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565478
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.bx1', '72.da1', '72.dt1', '72.fa1', '72.gi1', '72.gt1', '72.gv1', '72.gu1', '72.gw1', '72.gx1', '72.gy1', '72.gz1', '72.ha1', '72.kw1'], 'contains': ['288.bb1', '288.be1', '288.ga1', '288.gb1', '432.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.144.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ei1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565479
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '72.ct1', '72.du1', '72.ez1', '72.fm1', '72.gi1', '72.hd1', '72.he1', '72.hf1', '72.hg1', '72.hh1', '72.hi1', '72.hj1', '72.if1', '72.jk1'], 'contains': ['288.be1', '288.bf1', '288.bk1', '432.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 119750400, 87124129], 'label': '6912.ia.144.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ej1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565480
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bg1', '72.bz1', '72.dh1', '72.dv1', '72.em1', '72.fb1', '72.fn1', '72.fz1', '72.gj1', '72.gt1', '72.hd1', '72.hk1', '72.hl1', '72.hm1', '72.kz1'], 'contains': ['288.be1', '288.bh1', '288.gf1', '288.gh1', '288.gp1', '432.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 32929, 36933, 87305679948], 'label': '6912.ia.144.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ek1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565481
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '72.bn1', '72.dw1', '72.fa1', '72.fo1', '72.fy1', '72.hk1', '72.hn1', '72.ho1', '72.hp1', '72.hq1', '72.hr1', '72.ic1', '72.ig1', '72.kh1'], 'contains': ['288.be1', '288.bi1', '288.bo1', '432.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87124129, 87298041600], 'label': '6912.ia.144.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.el1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565482
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '72.cf1', '72.dc1', '72.dy1', '72.en1', '72.fd1', '72.fq1', '72.gb1', '72.gl1', '72.gv1', '72.hk1', '72.hu1', '72.hv1', '72.if1', '72.la1'], 'contains': ['288.be1', '288.bk1', '432.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43926348, 36933, 87124129], 'label': '6912.ia.144.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.en1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565483
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.cg1', '72.db1', '72.dx1', '72.em1', '72.fc1', '72.fp1', '72.ga1', '72.gk1', '72.gu1', '72.hj1', '72.hn1', '72.hs1', '72.ht1', '72.la1'], 'contains': ['288.be1', '288.bj1', '288.gg1', '288.gq1', '432.dc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87124129, 83480268], 'label': '6912.ia.144.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.em1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565484
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '8.c1', '8.e1', '8.g1'], 'contains': ['32.a1', '32.m1', '48.bq1', '48.br1', '48.bs1', '48.bt1', '64.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.16.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565485
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '72.ca1', '72.di1', '72.dz1', '72.en1', '72.fe1', '72.fr1', '72.gc1', '72.gm1', '72.gw1', '72.he1', '72.hn1', '72.hw1', '72.hx1', '72.kz1'], 'contains': ['288.be1', '288.bl1', '288.gh1', '288.gr1', '432.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 32929, 36933, 87265400268], 'label': '6912.ia.144.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eo1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565486
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '72.bv1', '72.da1', '72.du1', '72.el1', '72.fo1', '72.hl1', '72.hu1', '72.hs1', '72.hw1', '72.hy1', '72.hz1', '72.id1', '72.ih1', '72.kt1'], 'contains': ['288.be1', '288.bm1', '432.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.144.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ep1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565487
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.bz1', '72.dc1', '72.ea1', '72.et1', '72.ff1', '72.fs1', '72.gd1', '72.gn1', '72.gx1', '72.he1', '72.ic1', '72.hy1', '72.ia1', '72.lb1'], 'contains': ['288.be1', '288.bn1', '288.gi1', '288.gs1', '432.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87261771468, 87124129], 'label': '6912.ia.144.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eq1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565488
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '72.ca1', '72.db1', '72.eb1', '72.es1', '72.fg1', '72.ft1', '72.ge1', '72.go1', '72.gy1', '72.hd1', '72.hz1', '72.ib1', '72.ig1', '72.lb1'], 'contains': ['288.be1', '288.bo1', '432.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87222217548, 93405312000, 32929, 36933, 87124129], 'label': '6912.ia.144.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.er1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565489
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '72.by1', '72.cz1', '72.dw1', '72.ei1', '72.fm1', '72.hm1', '72.hv1', '72.ht1', '72.hx1', '72.ia1', '72.ib1', '72.ie1', '72.ii1', '72.kw1'], 'contains': ['288.be1', '288.bp1', '432.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87222200426, 36933, 87100665], 'label': '6912.ia.144.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.es1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565490
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.cb1', '72.dd1', '72.ed1', '72.eo1', '72.fh1', '72.fn1', '72.ga1', '72.gm1', '72.gx1', '72.hf1', '72.ho1', '72.hu1', '72.ib1', '72.lc1'], 'contains': ['288.be1', '288.gj1', '288.gk1', '432.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 19148, 36933, 40279680], 'label': '6912.ia.144.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.et1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565491
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.lc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '72.cc1', '72.de1', '72.ec1', '72.ep1', '72.fi1', '72.fr1', '72.gb1', '72.gj1', '72.gy1', '72.hg1', '72.hp1', '72.hs1', '72.ia1', '72.lc1'], 'contains': ['288.be1', '288.gk1', '432.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 93405312000, 36933, 40279680], 'label': '6912.ia.144.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565492
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.cd1', '72.de1', '72.dv1', '72.eq1', '72.fe1', '72.fv1', '72.gd1', '72.gp1', '72.gu1', '72.hh1', '72.hq1', '72.hv1', '72.hz1', '72.ld1'], 'contains': ['288.be1', '288.gl1', '288.gn1', '432.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178310348, 36933, 40279680], 'label': '6912.ia.144.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ev1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565493
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '72.cb1', '72.df1', '72.dx1', '72.eq1', '72.fd1', '72.fs1', '72.gg1', '72.go1', '72.gt1', '72.hg1', '72.hr1', '72.hx1', '72.id1', '72.le1'], 'contains': ['288.be1', '288.gm1', '432.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.144.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ew1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565494
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '72.cc1', '72.dg1', '72.dy1', '72.er1', '72.fc1', '72.ft1', '72.gf1', '72.gn1', '72.gw1', '72.hf1', '72.hm1', '72.hq1', '72.ih1', '72.le1'], 'contains': ['288.be1', '288.gt1', '432.dn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.144.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ex1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565495
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '8.b1', '8.g1', '8.h1'], 'contains': ['32.a1', '32.n1', '48.c1', '48.bu1', '48.bv1', '48.bw1', '64.d1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.16.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565496
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '72.ce1', '72.dd1', '72.dz1', '72.er1', '72.fb1', '72.fu1', '72.ge1', '72.gq1', '72.gv1', '72.hi1', '72.hr1', '72.ht1', '72.hy1', '72.ld1'], 'contains': ['288.be1', '288.gn1', '432.do1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305681228, 9465, 93405312000, 36933, 40279680], 'label': '6912.ia.144.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565497
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '72.cd1', '72.dg1', '72.ea1', '72.eo1', '72.fg1', '72.fp1', '72.fz1', '72.gl1', '72.ha1', '72.hi1', '72.hp1', '72.hw1', '72.ie1', '72.lf1'], 'contains': ['288.be1', '288.go1', '432.dp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87261772748], 'label': '6912.ia.144.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ez1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565498
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '72.ce1', '72.df1', '72.eb1', '72.ep1', '72.ff1', '72.fq1', '72.gc1', '72.gk1', '72.gz1', '72.hh1', '72.hl1', '72.ho1', '72.ii1', '72.lf1'], 'contains': ['288.be1', '288.gu1', '432.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87298060748], 'label': '6912.ia.144.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fa1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565499
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.bf1', '72.cf1', '72.dh1', '72.ec1', '72.es1', '72.fh1', '72.fu1', '72.gf1', '72.gp1', '72.gz1', '72.hj1', '72.ic1', '72.id1', '72.ie1'], 'contains': ['288.be1', '288.bg1', '288.ge1', '288.gv1', '432.dr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 127370880, 40312609, 93405312000, 36933], 'label': '6912.ia.144.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fb1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243565500
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '72.a1', '72.bg1', '72.cg1', '72.di1', '72.ed1', '72.et1', '72.fi1', '72.fv1', '72.gg1', '72.gq1', '72.ha1', '72.if1', '72.ig1', '72.ih1', '72.ii1'], 'contains': ['288.c1', '288.be1', '288.ge1', '432.ds1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 36933, 40279680], 'label': '6912.ia.144.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565501
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '72.cu1', '72.dn1', '72.ex1', '72.hd1', '72.ij1', '72.jl1'], 'contains': ['288.bf1', '288.bh1', '288.bo1', '432.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 43908480, 87178324129, 36933, 87091200], 'label': '6912.ia.144.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fe1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565502
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.cu1', '72.dr1', '72.fl1', '72.hj1', '72.ij1', '72.jk1'], 'contains': ['288.bf1', '288.bg1', '288.bj1', '432.dt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 93405312000, 40297548, 36933, 119750400], 'label': '6912.ia.144.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565503
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.ct1', '72.dq1', '72.ev1', '72.he1', '72.ij1', '72.jl1'], 'contains': ['288.bf1', '288.bl1', '288.bn1', '432.dv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218603809, 93405312000, 43908480, 36933, 87091200], 'label': '6912.ia.144.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ff1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565504
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '72.bo1', '72.do1', '72.ey1', '72.hk1', '72.ik1', '72.ki1'], 'contains': ['288.bh1', '288.bi1', '288.bk1', '432.ea1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 93405312000, 87178324129, 36933, 87091200], 'label': '6912.ia.144.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565505
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '72.ch1', '72.dh1', '72.eu1', '72.ij1', '72.ik1', '72.kz1'], 'contains': ['288.bh1', '288.bg1', '288.bl1', '288.gp1', '288.gr1', '432.dw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.144.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565506
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '8.c1', '8.f1', '8.h1'], 'contains': ['32.a1', '32.o1', '48.bx1', '48.by1', '48.bz1', '48.ca1', '64.e1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.16.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565507
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '72.ch1', '72.dj1', '72.eu1', '72.hd1', '72.hk1', '72.lg1'], 'contains': ['288.bh1', '288.bk1', '288.bo1', '432.ec1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 87178324129, 36933, 87091200], 'label': '6912.ia.144.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565508
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.bz1', '72.dj1', '72.em1', '72.ij1', '72.ik1', '72.lg1'], 'contains': ['288.bh1', '288.bj1', '288.bn1', '288.gw1', '288.gx1', '432.eb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178324129, 36933, 83471865, 87091200], 'label': '6912.ia.144.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565509
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '72.bu1', '72.cy1', '72.dn1', '72.do1', '72.eh1', '72.ks1'], 'contains': ['288.bh1', '288.bm1', '288.bp1', '432.ed1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 87265391865, 36933, 87091200], 'label': '6912.ia.144.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565510
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.bo1', '72.ds1', '72.fk1', '72.ic1', '72.ik1', '72.kh1'], 'contains': ['288.bi1', '288.bg1', '288.bn1', '432.dx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 93405312000, 40297548, 36933, 87298041600], 'label': '6912.ia.144.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565511
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '72.bn1', '72.dp1', '72.ew1', '72.hn1', '72.ik1', '72.ki1'], 'contains': ['288.bi1', '288.bj1', '288.bl1', '432.ee1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7653409, 87218603809, 93405312000, 36933, 87091200], 'label': '6912.ia.144.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565512
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '72.cf1', '72.dj1', '72.eu1', '72.hj1', '72.ik1', '72.la1'], 'contains': ['288.bg1', '288.bk1', '288.bj1', '432.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 127388748, 93405312000, 40297548, 36933], 'label': '6912.ia.144.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fi1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243565513
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '72.ch1', '72.dj1', '72.es1', '72.ic1', '72.ij1', '72.lb1'], 'contains': ['288.bg1', '288.bn1', '288.bo1', '432.dz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87222232609, 93405312000, 40297548, 36933], 'label': '6912.ia.144.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fj1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565514
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '72.ch1', '72.dc1', '72.en1', '72.he1', '72.ik1', '72.lg1'], 'contains': ['288.bk1', '288.bl1', '288.bn1', '432.eg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119768268, 87218603809, 93405312000, 36933, 87091200], 'label': '6912.ia.144.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565515
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '72.ca1', '72.db1', '72.eu1', '72.hn1', '72.ij1', '72.lg1'], 'contains': ['288.bj1', '288.bl1', '288.bo1', '432.ef1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218603809, 93405312000, 36933, 87091200, 83480268], 'label': '6912.ia.144.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '144.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243565516
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '72.b1', '72.h1', '72.ci1', '72.cm1', '72.ee1', '72.ef1', '72.fj1', '72.fw1', '72.gh1', '72.gr1', '72.hb1', '72.il1', '72.im1', '72.in1', '72.io1'], 'contains': ['288.d1', '432.ds1', '576.e1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.144.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565517
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '8.d1', '8.e1', '8.h1'], 'contains': ['32.a1', '32.p1', '48.cb1', '48.cc1', '48.cd1', '48.ce1', '64.f1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.16.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565518
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '72.cj1', '72.fx1', '72.gs1', '72.hc1', '72.ip1', '72.iq1', '72.lp1'], 'contains': ['288.hh1', '432.ds1', '576.f1'], 'core': '864.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40312609, 40297548, 36933, 93405314676, 40279680], 'label': '6912.ia.144.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.y1', 'old_label': '144.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565519
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '48.bn1', '72.ja1', '72.jf1', '72.jh1', '72.jk1', '72.jl1'], 'contains': ['288.a1', '288.i1', '288.bf1', '288.is1', '288.lx1', '432.ei1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 36933, 40279680], 'label': '6912.ia.144.fw1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565520
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.he1', '48.bn1', '48.bo1', '72.ir1', '72.jg1', '72.ji1'], 'contains': ['288.j1', '288.bq1', '288.bw1', '288.it1', '288.ly1', '432.ei1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 36933, 2676, 40279680], 'label': '6912.ia.144.fx1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565521
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hf1', '48.bn1', '48.bp1', '72.jj1'], 'contains': ['288.k1', '288.bu1', '288.bx1', '288.iu1', '288.lz1', '432.ei1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 127370880, 36933, 93405314676, 40279680], 'label': '6912.ia.144.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '144.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565522
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '48.br1', '72.jb1', '72.jf1', '72.jq1', '72.ju1', '72.jv1', '72.jx1', '72.ka1'], 'contains': ['288.a1', '288.n1', '288.r1', '288.iv1', '288.ma1', '432.ej1'], 'core': '288.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 36933, 40279680], 'label': '6912.ia.144.fz1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '144.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565523
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '48.bs1', '72.it1', '72.jm1', '72.jr1', '72.jt1', '72.jw1', '72.jy1', '72.kb1'], 'contains': ['288.b1', '288.mb1', '432.ej1', '576.q1'], 'core': '288.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.144.ga1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '144.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ga1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565524
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '48.bt1', '72.js1', '72.jz1', '72.kc1'], 'contains': ['288.by1', '288.mc1', '432.ej1', '576.r1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 40280426, 93452849280, 36933, 40279680], 'label': '6912.ia.144.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cg1', 'old_label': '144.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565525
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '48.br1', '48.bs1', '48.bt1', '72.iu1', '72.jg1', '72.kd1'], 'contains': ['288.o1', '288.s1', '288.bw1', '288.iw1', '288.md1', '432.ej1'], 'core': '864.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 40280426, 36933, 2676, 40279680], 'label': '6912.ia.144.gc1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '144.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565526
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ib1', '48.bu1', '48.bv1', '48.bw1', '72.ir1', '72.kd1', '72.ke1'], 'contains': ['288.p1', '288.br1', '288.bw1', '288.ix1', '288.me1', '432.ek1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87185911680, 36933, 2676, 40279680], 'label': '6912.ia.144.gd1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565527
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.bu1', '72.ja1', '72.jq1', '72.kg1', '72.kh1', '72.ki1'], 'contains': ['288.a1', '288.q1', '288.bi1', '288.iy1', '288.mf1', '432.ek1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 36933, 40279680], 'label': '6912.ia.144.ge1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ge1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565528
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '8.d1', '8.f1', '8.g1'], 'contains': ['32.a1', '32.q1', '48.cf1', '48.cg1', '48.ch1', '48.ci1', '48.cj1', '48.ck1', '48.cl1', '64.g1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.16.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565529
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.bv1', '72.is1', '72.jr1', '72.kf1', '72.kj1', '72.kk1'], 'contains': ['288.b1', '288.mg1', '432.ek1', '576.v1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87185911680, 47537280, 36933, 40279680], 'label': '6912.ia.144.gf1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565530
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.bw1', '72.js1', '72.kl1'], 'contains': ['288.by1', '288.mh1', '432.ek1', '576.w1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 87185911680, 93452849280, 36933, 40279680], 'label': '6912.ia.144.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '144.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565531
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1', '48.by1', '48.bz1', '72.it1', '72.jn1', '72.jt1', '72.kf1', '72.km1', '72.kn1', '72.ko1'], 'contains': ['288.b1', '288.mi1', '432.el1', '576.z1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.144.gh1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '144.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565532
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1', '48.ca1', '72.jb1', '72.jh1', '72.ju1', '72.kg1', '72.kp1', '72.kq1', '72.kr1'], 'contains': ['288.a1', '288.t1', '288.y1', '288.iz1', '288.mj1', '432.el1'], 'core': '288.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 87218571626, 36933, 40279680], 'label': '6912.ia.144.gi1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '144.hq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565533
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.iw1', '48.by1', '48.ca1', '72.iu1', '72.ji1', '72.ke1'], 'contains': ['288.u1', '288.z1', '288.bw1', '288.ja1', '288.mk1', '432.el1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87218571626, 36933, 2676, 40279680], 'label': '6912.ia.144.gj1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '144.hr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565534
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ix1', '48.bz1', '48.ca1', '72.jj1'], 'contains': ['288.v1', '288.ba1', '288.bx1', '288.jb1', '288.ml1', '432.el1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 87218571626, 36933, 93405314676, 40279680], 'label': '6912.ia.144.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '144.hs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565535
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1', '48.cc1', '48.cd1', '72.jc1', '72.jf1', '72.jv1', '72.kg1', '72.kp1', '72.ks1', '72.kt1'], 'contains': ['288.a1', '288.w1', '288.bm1', '288.jc1', '288.mm1', '432.em1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.144.gl1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.ht1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gl1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565536
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jc1', '48.cb1', '48.ce1', '72.iv1', '72.jg1', '72.ke1'], 'contains': ['288.x1', '288.bs1', '288.bw1', '288.jd1', '288.mn1', '432.em1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 43909226, 36933, 2676, 40279680], 'label': '6912.ia.144.gm1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.hu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565537
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1', '48.ce1', '72.iw1', '72.jm1', '72.jw1', '72.kf1', '72.km1', '72.ku1', '72.kv1'], 'contains': ['288.b1', '288.mo1', '432.em1', '576.bf1'], 'core': '288.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.144.gn1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '144.hv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565538
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jh1', '48.cd1', '48.ce1', '72.ix1'], 'contains': ['288.bz1', '288.mp1', '432.em1', '576.bg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 36933, 40279680], 'label': '6912.ia.144.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '144.hw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.go1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565539
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '8.i1', '8.l1', '8.m1'], 'contains': ['32.i1', '48.dh1', '48.do1', '48.dp1', '48.dq1', '64.b1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 93405312000, 9465, 7620480, 32929], 'label': '6912.ia.16.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565540
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1', '48.cg1', '48.ch1', '72.jc1', '72.jh1', '72.jq1', '72.jx1', '72.kq1', '72.ks1', '72.kw1'], 'contains': ['288.a1', '288.bb1', '288.bp1', '288.je1', '288.mq1', '432.en1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.144.gp1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.hx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565541
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jm1', '48.cf1', '48.ci1', '48.cj1', '72.iv1', '72.ji1', '72.kd1'], 'contains': ['288.bc1', '288.bt1', '288.bw1', '288.jf1', '288.mr1', '432.en1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.144.gq1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.hy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565542
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '48.ci1', '48.ck1', '72.iw1', '72.jn1', '72.jr1', '72.jy1', '72.kn1', '72.ku1', '72.kx1'], 'contains': ['288.b1', '288.ms1', '432.en1', '576.bm1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.144.gr1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '144.hz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565543
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jr1', '48.cf1', '48.ck1', '48.cl1', '72.jj1'], 'contains': ['288.bd1', '288.bv1', '288.bx1', '288.jg1', '288.mt1', '432.en1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 87222200426, 36933, 93405314676, 40279680], 'label': '6912.ia.144.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.ia1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565544
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '48.cj1', '48.cl1', '72.js1', '72.jz1', '72.ky1'], 'contains': ['288.by1', '288.mu1', '432.en1', '576.bo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.144.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.hq1', 'old_label': '144.ib1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gt1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565545
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ju1', '48.ch1', '48.ci1', '48.cl1', '72.ix1'], 'contains': ['288.bz1', '288.mv1', '432.en1', '576.bp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [120116474, 127370880, 87222200426, 36933, 40279680], 'label': '6912.ia.144.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ix1', 'old_label': '144.ic1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565546
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jv1', '48.ch1', '48.cj1', '48.ck1', '48.cl1'], 'contains': ['288.ca1', '288.mw1', '432.en1', '576.bq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 93525428474, 87222200426, 36933, 40279680], 'label': '6912.ia.144.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.gv1', 'old_label': '144.id1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565547
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.lc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '72.a1', '72.jd1', '72.jk1', '72.ka1', '72.kh1', '72.kr1', '72.kt1', '72.kw1', '72.kz1', '72.la1', '72.lb1', '72.lc1', '72.ld1', '72.le1', '72.lf1'], 'contains': ['288.a1', '288.be1', '288.bg1', '432.eo1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 40279680], 'label': '6912.ia.144.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.ie1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565548
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1', '72.jd1', '72.jl1', '72.ju1', '72.ki1', '72.ks1', '72.kz1', '72.lg1'], 'contains': ['288.a1', '288.bh1', '288.bl1', '432.ep1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87218603809, 93405312000, 36933, 40279680], 'label': '6912.ia.144.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.if1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565549
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1', '72.je1', '72.jk1', '72.jv1', '72.ki1', '72.kq1', '72.la1', '72.lg1'], 'contains': ['288.a1', '288.bk1', '288.bj1', '432.eq1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 93405312000, 36933, 40279680], 'label': '6912.ia.144.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ig1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565551
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1', '72.je1', '72.jl1', '72.jx1', '72.kh1', '72.kp1', '72.lb1', '72.lg1'], 'contains': ['288.a1', '288.bn1', '288.bo1', '432.er1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87222232609, 93405312000, 36933, 40279680], 'label': '6912.ia.144.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ih1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565552
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '72.c1', '72.iy1', '72.jo1', '72.kb1', '72.kj1', '72.ko1', '72.kv1', '72.kx1', '72.lh1', '72.li1', '72.lj1', '72.lk1', '72.ll1', '72.lm1', '72.ln1'], 'contains': ['288.b1', '432.eo1', '576.bx1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 40279680], 'label': '6912.ia.144.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.ii1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ha1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565553
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1', '72.iy1', '72.jp1', '72.jt1', '72.kk1', '72.ku1', '72.lh1', '72.lo1'], 'contains': ['288.b1', '432.ep1', '576.by1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87218603809, 47537280, 36933, 40279680], 'label': '6912.ia.144.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.ij1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565554
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1', '72.iz1', '72.jo1', '72.jw1', '72.kk1', '72.kn1', '72.li1', '72.lo1'], 'contains': ['288.b1', '432.eq1', '576.bz1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43941409, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.144.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.ik1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565555
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1', '72.iz1', '72.jp1', '72.jy1', '72.kj1', '72.km1', '72.lj1', '72.lo1'], 'contains': ['288.b1', '432.er1', '576.ca1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87222232609, 47537280, 36933, 40279680], 'label': '6912.ia.144.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.il1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565556
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '72.kc1', '72.kl1', '72.ky1', '72.lq1', '72.lr1', '72.ls1', '72.lt1'], 'contains': ['288.by1', '432.eo1', '576.cb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40312609, 93452849280, 36933, 40279680], 'label': '6912.ia.144.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bg1', 'old_label': '144.im1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.he1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565557
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1', '72.jz1', '72.kl1', '72.lq1'], 'contains': ['288.by1', '432.er1', '576.cc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87222232609, 93452849280, 36933, 40279680], 'label': '6912.ia.144.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '144.in1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hf1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565558
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.kd1', '48.df1', '72.d1'], 'contains': ['288.cs1', '288.cv1', '288.dc1', '288.dm1', '288.dp1', '288.en1', '288.eq1', '288.mx1', '432.fn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 2676, 87265382400], 'label': '6912.ia.144.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '144.io1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.io1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565559
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ke1', '48.dg1', '72.d1'], 'contains': ['288.cs1', '288.cx1', '288.cz1', '288.dn1', '288.dp1', '288.eo1', '288.ep1', '288.my1', '432.fo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 6851, 36933, 83468087, 87265382400], 'label': '6912.ia.144.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '144.ip1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ip1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565560
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.df1', '72.i1', '72.ne1', '72.nf1'], 'contains': ['288.ct1', '288.cu1', '288.db1', '288.dq1', '288.dt1', '288.dy1', '288.eu1', '288.mz1', '432.fn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 87265382400], 'label': '6912.ia.144.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565561
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1', '8.p1', '12.bl1', '12.bn1', '12.bo1', '16.h1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87178291200, 36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 7620480], 'label': '6912.ia.4.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '4.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565562
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '8.i1', '8.n1', '8.o1'], 'contains': ['32.i1', '48.ea1', '48.eb1', '48.ec1', '48.eh1', '64.d1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 47537280, 93405312000, 9465, 32929], 'label': '6912.ia.16.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565563
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dg1', '72.i1', '72.ne1', '72.ng1'], 'contains': ['288.ct1', '288.cw1', '288.cy1', '288.dr1', '288.dt1', '288.er1', '288.et1', '288.na1', '432.fo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 83468087, 87265382400], 'label': '6912.ia.144.ir1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.ir1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ir1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565564
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.nf1', '72.ng1', '72.nh1', '72.ni1', '72.nj1', '72.nk1'], 'contains': ['288.ct1', '288.de1', '288.dh1', '288.du1', '288.dx1', '288.ev1', '288.ey1', '432.fp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87265415329], 'label': '6912.ia.144.is1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.is1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.is1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565565
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.ne1', '72.nh1'], 'contains': ['288.ct1', '288.dg1', '288.df1', '288.dv1', '288.dx1', '288.ex1', '288.ew1', '432.fq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87265419333, 87100665], 'label': '6912.ia.144.it1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.it1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.it1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565566
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.bs1', '72.ne1'], 'contains': ['288.cu1', '288.cw1', '288.df1', '288.eb1', '288.ee1', '288.fd1', '288.fu1', '432.fr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 7656719, 93405312000, 36933, 87100665], 'label': '6912.ia.144.iu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565567
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.di1', '72.mk1', '72.bp1', '72.ne1'], 'contains': ['288.cu1', '288.cy1', '288.dg1', '288.ed1', '288.eh1', '288.fm1', '288.fr1', '432.fs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 87178300665], 'label': '6912.ia.144.iv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565568
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.bp1', '72.nf1'], 'contains': ['288.cu1', '288.db1', '288.dh1', '288.eg1', '288.eh1', '288.fq1', '288.fs1', '432.ft1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 87265391865, 36933], 'label': '6912.ia.144.iw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565569
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dj1', '72.mk1', '72.bs1', '72.nf1', '72.nm1', '72.nl1', '72.nn1', '72.no1'], 'contains': ['288.cu1', '288.de1', '288.ee1', '288.ek1', '288.ft1', '432.fu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7621226, 36933], 'label': '6912.ia.144.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ix1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ix1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565570
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.bp1', '72.ng1'], 'contains': ['288.cw1', '288.cy1', '288.dh1', '288.fc1', '288.fg1', '288.fm1', '288.fs1', '432.fv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 87265391865, 36933, 83468087], 'label': '6912.ia.144.iy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565571
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.bp1', '72.ne1'], 'contains': ['288.cw1', '288.db1', '288.dg1', '288.fe1', '288.fg1', '288.fq1', '288.fr1', '432.fw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 83468087, 87178300665], 'label': '6912.ia.144.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.iz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.iz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565572
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.bs1', '72.ng1', '72.nr1', '72.nq1', '72.ns1', '72.nt1'], 'contains': ['288.cw1', '288.de1', '288.fd1', '288.fh1', '288.ft1', '432.fx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 83498639], 'label': '6912.ia.144.ja1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ja1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ja1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565573
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '8.j1', '8.m1', '8.o1'], 'contains': ['32.i1', '48.f1', '48.em1', '48.en1', '48.eo1', '64.e1'], 'core': '48.f1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 47537280, 36933, 87178291946], 'label': '6912.ia.16.m1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565574
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.bx1', '72.ne1'], 'contains': ['288.cy1', '288.db1', '288.df1', '288.fn1', '288.fo1', '288.fx1', '288.gb1', '432.fy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.144.jb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.jb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565575
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dk1', '72.mk1', '72.bx1', '72.ng1', '72.nw1', '72.nv1', '72.nx1', '72.ny1'], 'contains': ['288.cy1', '288.de1', '288.fo1', '288.fp1', '288.ga1', '432.fz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87185912426], 'label': '6912.ia.144.jc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565576
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.bx1', '72.nf1', '72.oc1', '72.ob1', '72.od1', '72.oe1'], 'contains': ['288.db1', '288.de1', '288.fx1', '288.fy1', '288.ga1', '432.ga1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87261789839], 'label': '6912.ia.144.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565577
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dl1', '72.mp1', '72.bz1', '72.nh1', '72.nm1', '72.nr1', '72.nw1', '72.oc1'], 'contains': ['288.de1', '288.dg1', '288.gf1', '288.gi1', '288.gw1', '432.gc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87178300665], 'label': '6912.ia.144.jf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.je1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565578
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.cg1', '72.nh1', '72.nl1', '72.nq1', '72.nv1', '72.ob1'], 'contains': ['288.de1', '288.df1', '288.ge1', '288.gg1', '288.gq1', '432.gb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87100665, 87124129], 'label': '6912.ia.144.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.je1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565579
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.bz1', '72.nk1', '72.nn1', '72.ns1', '72.nx1', '72.od1'], 'contains': ['288.de1', '288.dh1', '288.gh1', '288.gi1', '288.gx1', '432.gd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87265400268], 'label': '6912.ia.144.jg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jg1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565580
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dm1', '72.mn1', '72.cb1', '72.ni1', '72.no1', '72.nq1', '72.nw1', '72.od1'], 'contains': ['288.de1', '288.gj1', '288.gm1', '432.ge1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7654690, 36933], 'label': '6912.ia.144.jh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565581
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mo1', '72.cb1', '72.nj1', '72.nl1', '72.nt1', '72.nx1', '72.oc1'], 'contains': ['288.de1', '288.gk1', '288.gm1', '432.gf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 83496610], 'label': '6912.ia.144.ji1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ji1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ji1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565582
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dn1', '72.mn1', '72.cd1', '72.nj1', '72.nm1', '72.ns1', '72.ny1', '72.ob1'], 'contains': ['288.de1', '288.gl1', '288.go1', '432.gg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87185945890], 'label': '6912.ia.144.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565583
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mo1', '72.cd1', '72.ni1', '72.nn1', '72.nr1', '72.nv1', '72.oe1'], 'contains': ['288.de1', '288.gn1', '288.go1', '432.gh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 87261787810, 9465, 93405312000, 36933], 'label': '6912.ia.144.jk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.jk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565584
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '8.k1', '8.l1', '8.o1'], 'contains': ['32.i1', '48.ep1', '48.et1', '48.eu1', '48.ew1', '64.f1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.16.n1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565585
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dh1', '48.do1', '72.mp1', '72.cg1', '72.nk1', '72.no1', '72.nt1', '72.ny1', '72.oe1'], 'contains': ['288.c1', '288.de1', '288.gg1', '432.gi1'], 'core': '288.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933], 'label': '6912.ia.144.jl1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.jl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565586
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.bz1', '72.nh1'], 'contains': ['288.dg1', '288.df1', '288.dh1', '288.gp1', '288.gw1', '288.gs1', '288.gx1', '432.gj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87100665, 87265415329], 'label': '6912.ia.144.jm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.p1', 'old_label': '144.jm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565587
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dh1', '48.dp1', '72.lw1', '72.ci1', '72.nd1', '72.np1', '72.nu1', '72.nz1', '72.of1'], 'contains': ['288.d1', '432.gi1', '576.k1'], 'core': '288.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 2676], 'label': '6912.ia.144.jn1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.jn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565588
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dh1', '48.dq1', '72.cj1', '72.oa1', '72.og1'], 'contains': ['288.hh1', '432.gi1', '576.l1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 93405314676], 'label': '6912.ia.144.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '144.jo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565589
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hg1', '48.di1', '72.lx1'], 'contains': ['288.di1', '288.dj1', '288.dl1', '288.ec1', '288.ei1', '288.fj1', '288.fv1', '432.fs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 47537280, 7621226, 36933, 87178300665], 'label': '6912.ia.144.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '144.jp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565590
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hh1', '48.dj1', '72.lx1', '72.oh1', '72.oi1'], 'contains': ['288.di1', '288.dk1', '288.ef1', '288.el1', '288.fw1', '432.fu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 47537280, 7621226, 36933], 'label': '6912.ia.144.jq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.jq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565591
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hi1', '48.dk1', '72.lx1', '72.oj1', '72.ok1'], 'contains': ['288.dj1', '288.dk1', '288.fk1', '288.fl1', '288.gc1', '432.fz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 47537280, 36933, 87185912426], 'label': '6912.ia.144.jr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.jr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565592
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hj1', '48.dl1', '72.lz1', '72.oh1', '72.oj1'], 'contains': ['288.dk1', '288.dl1', '288.gy1', '288.ha1', '288.hg1', '432.gc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 32929, 47537280, 36933, 87178300665], 'label': '6912.ia.144.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.js1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.js1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565593
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hk1', '48.dm1', '72.ly1', '72.oi1', '72.oj1'], 'contains': ['288.dk1', '288.hb1', '288.hd1', '432.ge1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 7654690, 47537280, 36933], 'label': '6912.ia.144.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.jt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565594
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hl1', '48.dn1', '72.ly1', '72.oh1', '72.ok1'], 'contains': ['288.dk1', '288.hc1', '288.he1', '432.gg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 47537280, 36933, 87185945890], 'label': '6912.ia.144.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ju1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ju1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565595
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '8.k1', '8.m1', '8.n1'], 'contains': ['32.i1', '48.ey1', '48.fc1', '48.fd1', '48.ff1', '48.fg1', '48.fh1', '48.fi1', '64.g1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.16.o1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565596
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '48.do1', '48.dp1', '48.dq1', '72.lz1', '72.oi1', '72.ok1'], 'contains': ['288.dk1', '288.gz1', '288.hf1', '432.gi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 9465, 32929, 47537280, 36933], 'label': '6912.ia.144.jv1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '144.jv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565597
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dr1', '72.h1', '72.cm1', '72.nd1', '72.ol1', '72.om1', '72.on1', '72.oo1'], 'contains': ['288.d1', '432.hc1', '576.n1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933, 2676], 'label': '6912.ia.144.jw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.jw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565598
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.cq1', '72.ne1'], 'contains': ['288.dq1', '288.dr1', '288.dv1', '288.eb1', '288.ed1', '288.fe1', '288.fn1', '432.gk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36239, 93405312000, 36933, 87265419333, 87100665], 'label': '6912.ia.144.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '144.jx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565599
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.cq1', '72.cr1'], 'contains': ['288.dq1', '288.ds1', '288.dw1', '288.eb1', '288.eg1', '288.ff1', '288.fz1', '432.gl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36239, 87305662080, 93405312000, 36933, 87100665], 'label': '6912.ia.144.jy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gs1', 'old_label': '144.jy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565600
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.ne1', '72.nf1'], 'contains': ['288.dq1', '288.dt1', '288.dx1', '288.ee1', '288.eh1', '288.fq1', '288.fx1', '432.gm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 7621226, 36933, 7629945, 87265382400], 'label': '6912.ia.144.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.jz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.jz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565601
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.cr1', '72.nf1', '72.op1', '72.oq1', '72.or1', '72.os1'], 'contains': ['288.dq1', '288.du1', '288.eg1', '288.ek1', '288.fy1', '432.gn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 36933, 746], 'label': '6912.ia.144.ka1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ka1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ka1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565602
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.ne1', '72.ng1'], 'contains': ['288.dr1', '288.dt1', '288.dx1', '288.fd1', '288.fg1', '288.fm1', '288.fo1', '432.go1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 7629945, 83468087, 87265382400], 'label': '6912.ia.144.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.kb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565603
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '72.cq1', '72.cx1'], 'contains': ['288.dr1', '288.ds1', '288.dw1', '288.fc1', '288.ff1', '288.fi1', '288.fn1', '432.gp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87305662080, 93405312000, 40280426, 36933, 87100665], 'label': '6912.ia.144.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gs1', 'old_label': '144.kc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565604
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '72.cx1', '72.ng1', '72.ot1', '72.ou1', '72.ov1', '72.ow1'], 'contains': ['288.dr1', '288.du1', '288.fc1', '288.fh1', '288.fp1', '432.gq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 40280426, 36933], 'label': '6912.ia.144.kd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.kd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565605
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.cr1', '72.cx1', '72.ox1', '72.oy1', '72.oz1', '72.pa1'], 'contains': ['288.ds1', '288.du1', '288.ff1', '288.fh1', '288.fy1', '432.gr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127407119, 9465, 87218570880, 93405312000, 36933], 'label': '6912.ia.144.ke1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.ke1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ke1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565606
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.p1'], 'contains': ['32.j1', '32.l1', '32.n1', '48.g1', '48.fr1', '48.fy1', '64.h1'], 'core': '48.g1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 93405312000, 47537280, 87178328133, 40279680], 'label': '6912.ia.16.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.p1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565607
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.cq1', '72.pb1'], 'contains': ['288.ds1', '288.dv1', '288.fe1', '288.fi1', '288.fz1', '432.gs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87265419333, 87100665], 'label': '6912.ia.144.kf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bm1', 'old_label': '144.kf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565748
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ju1', '48.fe1', '72.mi1'], 'contains': ['288.hn1', '432.jy1', '576.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40297548, 36933, 43548794, 87100665, 87261754346], 'label': '6912.ia.144.pc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.mi1', 'old_label': '144.pc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565608
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.nf1', '72.ng1', '72.pc1', '72.pd1', '72.pe1', '72.pf1'], 'contains': ['288.dt1', '288.du1', '288.fs1', '288.ft1', '288.ga1', '432.gt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87265419333, 83498639], 'label': '6912.ia.144.kg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.kg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kg1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565609
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.ne1', '72.pg1'], 'contains': ['288.dt1', '288.dv1', '288.fr1', '288.fu1', '288.gb1', '432.gu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7656719, 93405312000, 36933, 87265419333, 87100665], 'label': '6912.ia.144.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.kh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565610
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bg1', '72.dh1', '72.nh1', '72.op1', '72.ot1', '72.ox1', '72.pc1'], 'contains': ['288.du1', '288.dv1', '288.gf1', '288.ge1', '288.gp1', '432.gv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 36933, 87100665, 87124129, 87265382400], 'label': '6912.ia.144.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ki1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ki1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565611
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '72.dh1', '72.di1', '72.oq1', '72.ou1', '72.oy1', '72.oz1'], 'contains': ['288.du1', '288.dw1', '288.ge1', '288.gh1', '288.gr1', '432.gw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87305662080, 93405312000, 36933, 87100665, 87124129], 'label': '6912.ia.144.kj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.kj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kj1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565612
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.nh1', '72.nk1', '72.or1', '72.ov1', '72.pd1', '72.pe1'], 'contains': ['288.du1', '288.dx1', '288.gg1', '288.gi1', '288.gx1', '432.gx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 83480268, 87265415329], 'label': '6912.ia.144.kk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.kk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kk1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565613
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.dd1', '72.ni1', '72.os1', '72.ot1', '72.oy1', '72.pd1'], 'contains': ['288.du1', '288.gj1', '288.gn1', '432.gy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 34210, 36933], 'label': '6912.ia.144.kl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.kl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565614
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.de1', '72.nj1', '72.op1', '72.ow1', '72.oz1', '72.pe1'], 'contains': ['288.du1', '288.gk1', '288.gl1', '432.gz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 40313890, 36933], 'label': '6912.ia.144.km1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.km1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.km1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565615
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '72.dd1', '72.de1', '72.oq1', '72.ou1', '72.ox1', '72.pa1'], 'contains': ['288.du1', '288.gk1', '288.gn1', '432.ha1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 127405090, 87218570880, 93405312000, 36933], 'label': '6912.ia.144.kn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.kn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565616
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '72.ni1', '72.nj1', '72.or1', '72.ov1', '72.pc1', '72.pf1'], 'contains': ['288.du1', '288.gm1', '288.go1', '432.hb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 87265419333], 'label': '6912.ia.144.ko1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ko1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ko1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565617
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.p1'], 'contains': ['32.j1', '32.m1', '32.o1', '48.fs1', '48.fz1', '48.ga1', '64.i1'], 'core': '96.c1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 40280426, 47537280, 87178328133, 40279680], 'label': '6912.ia.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.q1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565618
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dr1', '72.bg1', '72.di1', '72.nk1', '72.os1', '72.ow1', '72.pa1', '72.pf1'], 'contains': ['288.c1', '288.du1', '288.gh1', '432.hc1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933], 'label': '6912.ia.144.kp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.kp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565619
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '72.nh1', '72.pb1'], 'contains': ['288.dv1', '288.dx1', '288.gw1', '288.gq1', '288.gs1', '432.hd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7653409, 93405312000, 36933, 87265419333, 87100665], 'label': '6912.ia.144.kq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '144.kq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565620
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '72.pb1', '72.pg1'], 'contains': ['288.dv1', '288.gt1', '288.gu1', '432.he1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43942690, 36933, 87265419333, 87100665], 'label': '6912.ia.144.kr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.kr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565621
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '72.dh1', '72.pg1'], 'contains': ['288.dv1', '288.dw1', '288.gp1', '288.gr1', '288.gv1', '432.hf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87305662080, 93405312000, 36933, 87124129], 'label': '6912.ia.144.ks1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bp1', 'old_label': '144.ks1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ks1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565622
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.dt1', '72.ne1'], 'contains': ['288.dy1', '288.eb1', '288.eh1', '288.er1', '288.ew1', '288.fg1', '288.gb1', '432.hg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185947919, 87185911680, 93405312000, 36933, 87100665], 'label': '6912.ia.144.kt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.kt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565623
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hm1', '48.ds1', '72.lx1'], 'contains': ['288.dz1', '288.ec1', '288.ef1', '288.es1', '288.fa1', '288.fk1', '288.fv1', '432.hh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 7621226, 36933, 7629945, 87178300665], 'label': '6912.ia.144.ku1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '144.ku1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ku1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565624
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ds1', '72.mk1', '72.dk1', '72.ne1'], 'contains': ['288.dy1', '288.ed1', '288.ee1', '288.et1', '288.ex1', '288.fo1', '288.fr1', '432.hh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 7621226, 36933, 7629945, 87178300665], 'label': '6912.ia.144.kv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.kv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565625
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.dk1', '72.nf1'], 'contains': ['288.dy1', '288.ee1', '288.eg1', '288.eu1', '288.ey1', '288.fs1', '288.fx1', '432.hi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 7621226, 87265391865, 36933, 7629945], 'label': '6912.ia.144.kw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.kw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565626
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dt1', '72.mk1', '72.dt1', '72.nf1', '72.pi1', '72.ph1', '72.pj1', '72.pk1'], 'contains': ['288.dy1', '288.eh1', '288.ek1', '288.ev1', '288.ga1', '432.hj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87185912426], 'label': '6912.ia.144.kx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.kx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565901
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1', '96.dm1', '96.du1', '96.dv1'], 'contains': ['384.h1', '384.w1', '576.cm1', '576.cn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87185948613, 87128133, 2676], 'label': '6912.ia.192.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.cy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565627
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hp1', '48.dt1', '72.lx1', '72.pl1', '72.pm1'], 'contains': ['288.dz1', '288.ei1', '288.el1', '288.ez1', '288.gc1', '432.hj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 47537280, 36933, 87185912426], 'label': '6912.ia.144.ky1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ky1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ky1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565628
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '8.p1'], 'contains': ['32.j1', '32.p1', '32.q1', '48.ft1', '48.gb1', '48.gc1', '48.gd1', '64.j1'], 'core': '96.c1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 87178291200, 47537280, 43944719, 40279680], 'label': '6912.ia.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.r1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565629
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hq1', '48.dt1', '72.pn1'], 'contains': ['288.ea1', '288.ej1', '288.em1', '288.fb1', '288.gd1', '432.hj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 87185911680, 93452849280, 36933, 87185912426], 'label': '6912.ia.144.kz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '144.kz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.kz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565630
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.du1', '72.ms1', '72.dv1', '72.nm1', '72.op1', '72.pi1'], 'contains': ['288.ek1', '288.gf1', '288.gl1', '432.hl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 36933, 746], 'label': '6912.ia.144.lb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.la1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565631
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mq1', '72.ec1', '72.ed1', '72.nl1', '72.op1', '72.oq1', '72.ph1'], 'contains': ['288.ek1', '288.ge1', '288.gk1', '432.hk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 746], 'label': '6912.ia.144.la1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.lb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.la1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565632
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dv1', '72.mr1', '72.dx1', '72.nl1', '72.no1', '72.or1', '72.pi1', '72.pj1'], 'contains': ['288.ek1', '288.gg1', '288.gm1', '432.hm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83495329, 83496610], 'label': '6912.ia.144.lc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565633
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mq1', '72.dv1', '72.dz1', '72.nn1', '72.oq1', '72.os1', '72.pj1'], 'contains': ['288.ek1', '288.gh1', '288.gn1', '432.hn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218603809, 93405312000, 36933, 746], 'label': '6912.ia.144.ld1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ld1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ld1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565634
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dw1', '72.mr1', '72.ea1', '72.nm1', '72.nn1', '72.or1', '72.ph1', '72.pk1'], 'contains': ['288.ek1', '288.gi1', '288.go1', '432.ho1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87261787810, 9465, 93405312000, 36933, 87261786529], 'label': '6912.ia.144.le1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.le1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.le1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565635
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.dx1', '72.ms1', '72.ed1', '72.no1', '72.os1', '72.pk1'], 'contains': ['288.c1', '288.ek1', '288.gj1', '432.hp1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 746], 'label': '6912.ia.144.lf1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.lf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lf1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565636
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hv1', '48.du1', '72.mb1', '72.oh1', '72.pl1'], 'contains': ['288.el1', '288.gy1', '288.hc1', '432.hl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 47537280, 36933, 746], 'label': '6912.ia.144.lg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.lg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565637
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hw1', '48.dv1', '72.ma1', '72.oi1', '72.pl1'], 'contains': ['288.el1', '288.gz1', '288.hd1', '432.hm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.144.lh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.lh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565638
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hx1', '48.dw1', '72.ma1', '72.oh1', '72.pm1'], 'contains': ['288.el1', '288.ha1', '288.he1', '432.ho1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87261787810, 9465, 79870533, 36933, 87261786529], 'label': '6912.ia.144.li1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.li1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.li1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565639
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.p1'], 'contains': ['32.l1', '32.m1', '32.p1', '48.gi1', '48.gk1', '48.gl1', '64.l1'], 'core': '96.d1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 93405312000, 47537280, 43944719, 40279680], 'label': '6912.ia.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.s1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243565640
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hy1', '48.dx1', '48.dy1', '72.mb1', '72.oi1', '72.pm1'], 'contains': ['288.el1', '288.hb1', '288.hf1', '432.hp1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 32929, 47537280, 36933, 746], 'label': '6912.ia.144.lj1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.lj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565641
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.hz1', '48.dw1', '72.pn1'], 'contains': ['288.em1', '288.hi1', '288.hk1', '432.ho1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87261787810, 9465, 93485182533, 36933, 87261786529], 'label': '6912.ia.144.lk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '144.lk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lk1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565642
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ia1', '48.dx1', '48.dz1', '72.pn1'], 'contains': ['288.em1', '288.hj1', '288.hl1', '432.hp1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9465, 32929, 93452849280, 36933, 746], 'label': '6912.ia.144.ll1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '144.ll1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ll1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565643
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ea1', '48.eb1', '48.ec1', '72.lw1', '72.ef1', '72.nd1', '72.po1', '72.pp1', '72.pq1', '72.pr1'], 'contains': ['288.d1', '432.id1', '576.t1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 2676], 'label': '6912.ia.144.lm1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.lm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565644
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.dk1', '72.ng1'], 'contains': ['288.er1', '288.et1', '288.ey1', '288.fc1', '288.fd1', '288.fo1', '288.fs1', '432.hq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87265391865, 36933, 7629945, 83468087], 'label': '6912.ia.144.ln1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.ln1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ln1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565645
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.dk1', '72.ne1'], 'contains': ['288.er1', '288.eu1', '288.ex1', '288.fd1', '288.fe1', '288.fr1', '288.fx1', '432.hr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 7629945, 83468087, 87178300665], 'label': '6912.ia.144.lo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.lo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565646
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.dt1', '72.ng1', '72.pt1', '72.ps1', '72.pu1', '72.pv1'], 'contains': ['288.er1', '288.ev1', '288.fg1', '288.fh1', '288.ga1', '432.hs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87261789839], 'label': '6912.ia.144.lp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565647
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ic1', '48.ed1', '72.lx1', '72.pw1', '72.px1'], 'contains': ['288.es1', '288.ez1', '288.fj1', '288.fl1', '288.fw1', '432.hu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 47537280, 7621226, 36933], 'label': '6912.ia.144.lq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.lq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565648
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '72.ek1', '72.ne1'], 'contains': ['288.et1', '288.eu1', '288.ew1', '288.fm1', '288.fn1', '288.fq1', '288.fu1', '432.ht1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7656719, 87185911680, 93405312000, 36933, 87100665], 'label': '6912.ia.144.lr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '144.lr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565649
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ed1', '72.mk1', '72.ek1', '72.ng1', '72.pz1', '72.py1', '72.qa1', '72.qb1'], 'contains': ['288.et1', '288.ev1', '288.fm1', '288.fp1', '288.ft1', '432.hu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 7621226, 36933], 'label': '6912.ia.144.ls1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ls1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ls1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565650
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '8.p1'], 'contains': ['32.l1', '32.o1', '32.q1', '48.gj1', '48.gm1', '48.gn1', '48.go1', '64.m1'], 'core': '96.d1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 93405312000, 47537280, 87222235919, 40279680], 'label': '6912.ia.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.t1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565651
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '72.ek1', '72.nf1', '72.qd1', '72.qc1', '72.qe1', '72.qf1'], 'contains': ['288.eu1', '288.ev1', '288.fq1', '288.ft1', '288.fy1', '432.hv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 83498639], 'label': '6912.ia.144.lt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lt1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565652
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ee1', '72.mp1', '72.em1', '72.nh1', '72.pi1', '72.pt1', '72.pz1', '72.qd1'], 'contains': ['288.ev1', '288.ex1', '288.gf1', '288.gg1', '288.gw1', '432.hx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 83480268, 87178300665], 'label': '6912.ia.144.lv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565653
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.et1', '72.nh1', '72.ph1', '72.ps1', '72.py1', '72.qc1'], 'contains': ['288.ev1', '288.ew1', '288.ge1', '288.gi1', '288.gs1', '432.hw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87100665, 87124129], 'label': '6912.ia.144.lu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lu1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565654
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.em1', '72.nk1', '72.pj1', '72.pu1', '72.qa1', '72.qe1'], 'contains': ['288.ev1', '288.ey1', '288.gg1', '288.gh1', '288.gx1', '432.hy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87265400268, 83480268], 'label': '6912.ia.144.lw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565655
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ef1', '72.mn1', '72.eo1', '72.ni1', '72.pk1', '72.ps1', '72.pz1', '72.qe1'], 'contains': ['288.ev1', '288.gj1', '288.go1', '432.hz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 87185945890], 'label': '6912.ia.144.lx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565656
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mo1', '72.eo1', '72.nj1', '72.ph1', '72.pv1', '72.qa1', '72.qd1'], 'contains': ['288.ev1', '288.gk1', '288.go1', '432.ia1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87261787810, 9465, 87185911680, 93405312000, 36933], 'label': '6912.ia.144.ly1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ly1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ly1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565657
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.eg1', '72.mn1', '72.eq1', '72.nj1', '72.pi1', '72.pu1', '72.qb1', '72.qc1'], 'contains': ['288.ev1', '288.gl1', '288.gm1', '432.ib1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 7654690, 36933], 'label': '6912.ia.144.lz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.lz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.lz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565658
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mo1', '72.eq1', '72.ni1', '72.pj1', '72.pt1', '72.py1', '72.qf1'], 'contains': ['288.ev1', '288.gm1', '288.gn1', '432.ic1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 36933, 83496610], 'label': '6912.ia.144.ma1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ma1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ma1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565659
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ea1', '48.eh1', '72.mp1', '72.et1', '72.nk1', '72.pk1', '72.pv1', '72.qb1', '72.qf1'], 'contains': ['288.c1', '288.ev1', '288.gi1', '432.id1'], 'core': '288.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933], 'label': '6912.ia.144.mb1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.mb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565660
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '72.em1', '72.nh1'], 'contains': ['288.ex1', '288.ew1', '288.ey1', '288.gp1', '288.gw1', '288.gq1', '288.gx1', '432.ie1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 93405312000, 36933, 87100665, 87265415329], 'label': '6912.ia.144.mc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.p1', 'old_label': '144.mc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565661
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.p1'], 'contains': ['32.m1', '32.n1', '32.q1', '48.gp1', '48.gq1', '48.gr1', '48.gs1', '64.n1'], 'core': '96.e1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 93405312000, 47537280, 87222235919, 40279680], 'label': '6912.ia.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.u1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565662
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ii1', '48.ee1', '72.lz1', '72.pl1', '72.pw1'], 'contains': ['288.ez1', '288.fa1', '288.gy1', '288.gz1', '288.hg1', '432.hx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [32929, 79833600, 36933, 83480268, 87178300665], 'label': '6912.ia.144.md1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.md1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.md1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565663
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ij1', '48.ef1', '72.ly1', '72.pm1', '72.pw1'], 'contains': ['288.ez1', '288.hb1', '288.he1', '432.hz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 47537280, 36933, 87185945890], 'label': '6912.ia.144.me1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.me1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.me1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565664
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ik1', '48.eg1', '72.ly1', '72.pl1', '72.px1'], 'contains': ['288.ez1', '288.hc1', '288.hd1', '432.ib1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87185911680, 7654690, 47537280, 36933], 'label': '6912.ia.144.mf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.mf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565665
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.il1', '48.eb1', '48.eh1', '72.lz1', '72.pm1', '72.px1'], 'contains': ['288.ez1', '288.ha1', '288.hf1', '432.id1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 47537280, 36933], 'label': '6912.ia.144.mg1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '144.mg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565668
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mw1', '72.dv1', '72.fb1', '72.nr1', '72.ot1', '72.ox1', '72.pt1'], 'contains': ['288.fh1', '288.gf1', '288.gn1', '432.ih1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 87178324129, 36933], 'label': '6912.ia.144.ml1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.mj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ml1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565669
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mt1', '72.ed1', '72.fh1', '72.nq1', '72.ot1', '72.oy1', '72.ps1'], 'contains': ['288.fh1', '288.ge1', '288.gj1', '432.if1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 127371626], 'label': '6912.ia.144.mj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.mk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565670
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mu1', '72.ec1', '72.fh1', '72.fi1', '72.ou1', '72.ox1', '72.oz1'], 'contains': ['288.fh1', '288.ge1', '288.gk1', '432.ig1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 40280426, 36933], 'label': '6912.ia.144.mk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.ml1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mk1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565671
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mv1', '72.dx1', '72.nq1', '72.nt1', '72.ov1', '72.pt1', '72.pu1'], 'contains': ['288.fh1', '288.gg1', '288.gm1', '432.ii1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 83495329], 'label': '6912.ia.144.mm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.mm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mm1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565672
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.k1', '3456.m1', '3456.g1', '3456.i1', '3456.j1', '3456.l1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '6.a1', '6.l1', '6.o1', '8.b1', '8.i1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.d1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243565673
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.i1', '8.j1', '8.k1', '8.l1', '8.m1', '8.n1', '8.o1', '12.dp1', '12.dq1', '12.ds1', '16.h1'], 'core': '24.e1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87178291200, 36933, 47537280, 93405312000, 9465, 7620480, 32929, 7621226], 'label': '6912.ia.4.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '4.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565674
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.h1', '8.p1'], 'contains': ['32.n1', '32.o1', '32.p1', '48.gt1', '48.gu1', '48.gv1', '64.o1'], 'core': '96.e1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 93405312000, 47537280, 43944719, 40279680], 'label': '6912.ia.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '16.v1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565675
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mt1', '72.dv1', '72.fe1', '72.ns1', '72.ow1', '72.oz1', '72.pu1'], 'contains': ['288.fh1', '288.gh1', '288.gl1', '432.ij1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218603809, 93405312000, 40280426, 36933], 'label': '6912.ia.144.mn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.mn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mn1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565676
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mu1', '72.dz1', '72.fb1', '72.fe1', '72.ou1', '72.oy1', '72.pa1'], 'contains': ['288.fh1', '288.gh1', '288.gn1', '432.ik1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127407119, 9465, 87218603809, 93405312000, 36933], 'label': '6912.ia.144.mo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.mo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mo1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565677
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mv1', '72.ea1', '72.nr1', '72.ns1', '72.ov1', '72.ps1', '72.pv1'], 'contains': ['288.fh1', '288.gi1', '288.go1', '432.il1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87185945890, 87261786529], 'label': '6912.ia.144.mp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.mp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565678
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ei1', '72.mw1', '72.ed1', '72.fi1', '72.nt1', '72.ow1', '72.pa1', '72.pv1'], 'contains': ['288.c1', '288.fh1', '288.gk1', '432.im1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 40280426, 36933], 'label': '6912.ia.144.mq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.mq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565679
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mx1', '72.fc1', '72.pb1'], 'contains': ['288.fi1', '288.gq1', '288.gt1', '432.in1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 93405312000, 43942690, 36933, 87100665], 'label': '6912.ia.144.mr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '144.mr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mr1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565680
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ms1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mx1', '72.ff1', '72.pb1'], 'contains': ['288.fi1', '288.gs1', '288.gu1', '432.io1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185944609, 93405312000, 36933, 87222233890, 87100665], 'label': '6912.ia.144.ms1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '144.ms1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ms1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565681
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ei1', '72.md1', '72.ee1', '72.fj1', '72.nu1', '72.om1', '72.on1', '72.pp1'], 'contains': ['288.d1', '432.im1', '576.y1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 40280426, 36933, 2676], 'label': '6912.ia.144.mt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.mt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565682
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.io1', '48.ej1', '72.mb1', '72.oj1', '72.pw1'], 'contains': ['288.fl1', '288.gy1', '288.hb1', '432.iq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 47537280, 34210, 36933], 'label': '6912.ia.144.mu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.mu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mu1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565683
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ip1', '48.ek1', '72.ma1', '72.ok1', '72.pw1'], 'contains': ['288.fl1', '288.gz1', '288.he1', '432.ir1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87261787810, 9465, 79870533, 36933, 83495329], 'label': '6912.ia.144.mv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.mv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565684
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.iq1', '48.el1', '72.ma1', '72.oj1', '72.px1'], 'contains': ['288.fl1', '288.ha1', '288.hd1', '432.it1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83496610, 87261786529], 'label': '6912.ia.144.mw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.mw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565685
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.d1', '36.e1', '36.g1', '36.jw1', '36.jx1', '36.bz1', '36.cj1', '36.ef1', '36.ej1', '36.kd1', '36.ke1', '54.b1', '72.d1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565686
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ir1', '48.em1', '48.en1', '48.eo1', '72.mb1', '72.ok1', '72.px1'], 'contains': ['288.fl1', '288.hc1', '288.hf1', '432.iu1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 32929, 47537280, 36933, 87178291946], 'label': '6912.ia.144.mx1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.mx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mx1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566643
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ea1', '144.ph1'], 'contains': ['576.cv1', '576.cy1', '576.db1', '864.en1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [119759865, 93405312000, 87128133, 87261759287], 'label': '6912.ia.288.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '288.mw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ip1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565687
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.mz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ej1', '72.ms1', '72.fn1', '72.nw1', '72.ot1', '72.pz1'], 'contains': ['288.fp1', '288.gf1', '288.gj1', '432.iq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 34210, 36933], 'label': '6912.ia.144.mz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.my1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.mz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565688
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.my1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mq1', '72.fu1', '72.fv1', '72.nv1', '72.ot1', '72.ou1', '72.py1'], 'contains': ['288.fp1', '288.ge1', '288.gn1', '432.ip1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 36933, 87178291946], 'label': '6912.ia.144.my1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.mz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.my1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565689
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.na1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ek1', '72.mr1', '72.fp1', '72.nv1', '72.ny1', '72.ov1', '72.pz1', '72.qa1'], 'contains': ['288.fp1', '288.gg1', '288.go1', '432.ir1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87261787810, 9465, 93405312000, 36933, 83495329], 'label': '6912.ia.144.na1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.na1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.na1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565690
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mq1', '72.fn1', '72.fr1', '72.nx1', '72.ou1', '72.ow1', '72.qa1'], 'contains': ['288.fp1', '288.gh1', '288.gk1', '432.is1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218603809, 93405312000, 40313890, 36933], 'label': '6912.ia.144.nb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.nb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565691
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.el1', '72.mr1', '72.fs1', '72.nw1', '72.nx1', '72.ov1', '72.py1', '72.qb1'], 'contains': ['288.fp1', '288.gi1', '288.gm1', '432.it1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83496610, 87261786529], 'label': '6912.ia.144.nc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565692
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '48.em1', '72.ms1', '72.fv1', '72.ny1', '72.ow1', '72.qb1'], 'contains': ['288.c1', '288.fp1', '288.gl1', '432.iu1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 87178291946], 'label': '6912.ia.144.nd1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '144.nd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565693
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ne1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '48.en1', '72.mc1', '72.fw1', '72.nz1', '72.om1', '72.pq1'], 'contains': ['288.d1', '432.iu1', '576.bb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 36933, 2676, 87178291946], 'label': '6912.ia.144.ne1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.ne1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ne1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565694
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '48.eo1', '72.fx1', '72.oa1'], 'contains': ['288.hh1', '432.iu1', '576.bc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 32929, 36933, 93405314676, 87178291946], 'label': '6912.ia.144.nf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1', 'old_label': '144.nf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565695
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.eq1', '72.nb1', '72.fz1', '72.nm1', '72.nr1', '72.pc1', '72.pz1', '72.qd1'], 'contains': ['288.ft1', '288.gf1', '288.go1', '432.iw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 36933, 83498639], 'label': '6912.ia.144.nh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ng1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565696
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.d1', '36.f1', '36.i1', '36.ce1', '36.cp1', '36.ei1', '36.ek1', '54.d1', '72.e1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 43909226, 32929, 87178291200, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565697
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ng1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.my1', '72.gg1', '72.nl1', '72.nq1', '72.pc1', '72.py1', '72.qc1'], 'contains': ['288.ft1', '288.ge1', '288.gm1', '432.iv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.144.ng1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ng1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565698
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ni1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.er1', '72.mz1', '72.ga1', '72.no1', '72.nq1', '72.pd1', '72.pz1', '72.qe1'], 'contains': ['288.ft1', '288.gg1', '288.gj1', '432.ix1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83498639, 83495329], 'label': '6912.ia.144.ni1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ni1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ni1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565699
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.na1', '72.ga1', '72.nl1', '72.nt1', '72.pe1', '72.qa1', '72.qd1'], 'contains': ['288.ft1', '288.gg1', '288.gk1', '432.iy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7621226, 36933, 83495329], 'label': '6912.ia.144.nj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565700
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.my1', '72.fz1', '72.nn1', '72.ns1', '72.pf1', '72.qa1', '72.qe1'], 'contains': ['288.ft1', '288.gh1', '288.go1', '432.iz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83498639, 87265415329], 'label': '6912.ia.144.nk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nk1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565701
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.es1', '72.mz1', '72.gd1', '72.nm1', '72.ns1', '72.pe1', '72.qb1', '72.qc1'], 'contains': ['288.ft1', '288.gi1', '288.gl1', '432.ja1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83498639, 87261786529], 'label': '6912.ia.144.nl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nl1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565702
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.na1', '72.gd1', '72.nn1', '72.nr1', '72.pd1', '72.py1', '72.qf1'], 'contains': ['288.ft1', '288.gi1', '288.gn1', '432.jb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7621226, 36933, 87261786529], 'label': '6912.ia.144.nm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565703
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ep1', '48.et1', '48.eu1', '72.nb1', '72.gg1', '72.no1', '72.nt1', '72.pf1', '72.qb1', '72.qf1'], 'contains': ['288.c1', '288.ft1', '288.gm1', '432.jc1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 7621226, 36933], 'label': '6912.ia.144.nn1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.nn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nn1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565704
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.no1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nc1', '72.gc1', '72.pg1'], 'contains': ['288.fu1', '288.gr1', '288.gu1', '432.jd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7656719, 93405312000, 36933, 87305695009, 87100665], 'label': '6912.ia.144.no1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '144.no1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.no1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565705
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.np1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ev1', '72.nc1', '72.gf1', '72.pg1'], 'contains': ['288.fu1', '288.gt1', '288.gv1', '432.je1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 40297548, 36933, 87100665, 83463146], 'label': '6912.ia.144.np1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '144.np1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.np1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565706
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ep1', '48.ew1', '72.me1', '72.gh1', '72.np1', '72.nu1', '72.oo1', '72.pq1', '72.pr1'], 'contains': ['288.d1', '432.jc1', '576.be1'], 'core': '288.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 32929, 7621226, 36933, 2676], 'label': '6912.ia.144.nq1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.nq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565707
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '9.a1'], 'contains': ['36.e1', '36.h1', '36.i1', '36.eg1', '36.eh1', '36.fp1', '36.fq1', '54.f1', '72.f1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 43908480, 2676, 87109068, 87124129, 32929], 'label': '6912.ia.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565708
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jd1', '48.eq1', '72.mg1', '72.oh1', '72.pw1'], 'contains': ['288.fw1', '288.gy1', '288.he1', '432.iw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 79870533, 36933, 83498639], 'label': '6912.ia.144.nr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.nr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565709
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ns1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.je1', '48.er1', '72.mf1', '72.oi1', '72.pw1'], 'contains': ['288.fw1', '288.gz1', '288.hb1', '432.ix1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.144.ns1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.ns1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ns1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565710
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jf1', '48.es1', '72.mf1', '72.oh1', '72.px1'], 'contains': ['288.fw1', '288.ha1', '288.hc1', '432.ja1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83498639, 87261786529], 'label': '6912.ia.144.nt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.nt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nt1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565711
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jg1', '48.et1', '48.ew1', '72.mg1', '72.oi1', '72.px1'], 'contains': ['288.fw1', '288.hd1', '288.hf1', '432.jc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 32929, 47537280, 7621226, 36933], 'label': '6912.ia.144.nu1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '144.nu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nu1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565712
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jh1', '48.eu1', '48.ew1', '72.mh1'], 'contains': ['288.hm1', '432.jc1', '576.bg1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 9465, 32929, 7621226, 36933], 'label': '6912.ia.144.nv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dn1', 'old_label': '144.nv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565713
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jh1', '48.ev1', '72.mi1'], 'contains': ['288.hn1', '432.je1', '576.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40297548, 36933, 43548794, 87100665, 83463146], 'label': '6912.ia.144.nw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '144.nw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565714
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mw1', '72.fn1', '72.gj1', '72.oc1', '72.op1', '72.ox1', '72.qd1'], 'contains': ['288.fy1', '288.gf1', '288.gk1', '432.jh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 40313890, 36933], 'label': '6912.ia.144.nz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.nx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565715
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.nx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mt1', '72.fv1', '72.gp1', '72.ob1', '72.op1', '72.oz1', '72.qc1'], 'contains': ['288.fy1', '288.ge1', '288.gl1', '432.jf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 87305662826, 93405312000, 36933], 'label': '6912.ia.144.nx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ny1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.nx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565716
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ny1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mu1', '72.fu1', '72.gp1', '72.gq1', '72.oq1', '72.ox1', '72.oy1'], 'contains': ['288.fy1', '288.ge1', '288.gn1', '432.jg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 87218571626, 36933], 'label': '6912.ia.144.ny1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.nz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ny1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565717
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mv1', '72.fp1', '72.ob1', '72.oe1', '72.or1', '72.qd1', '72.qe1'], 'contains': ['288.fy1', '288.gg1', '288.go1', '432.ji1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87185945890, 83495329], 'label': '6912.ia.144.oa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.oa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oa1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565718
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.f1', '36.g1', '36.h1', '36.ff1', '36.fg1', '36.fw1', '36.gb1', '54.h1', '72.g1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 2676, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565719
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ob1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mt1', '72.fn1', '72.gm1', '72.od1', '72.os1', '72.oy1', '72.qe1'], 'contains': ['288.fy1', '288.gh1', '288.gj1', '432.jj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218603809, 93405312000, 34210, 36933], 'label': '6912.ia.144.ob1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.ob1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ob1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565720
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mu1', '72.fr1', '72.gj1', '72.gm1', '72.oq1', '72.oz1', '72.pa1'], 'contains': ['288.fy1', '288.gh1', '288.gk1', '432.jk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 127405090, 87218603809, 93405312000, 36933], 'label': '6912.ia.144.oc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '144.oc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565721
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.od1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mv1', '72.fs1', '72.oc1', '72.od1', '72.or1', '72.qc1', '72.qf1'], 'contains': ['288.fy1', '288.gi1', '288.gm1', '432.jl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 87261786529], 'label': '6912.ia.144.od1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.od1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.od1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565722
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ex1', '72.mw1', '72.fv1', '72.gq1', '72.oe1', '72.os1', '72.pa1', '72.qf1'], 'contains': ['288.c1', '288.fy1', '288.gn1', '432.jm1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87218571626, 36933], 'label': '6912.ia.144.oe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '144.oe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oe1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565723
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.of1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mx1', '72.gk1', '72.pb1'], 'contains': ['288.fz1', '288.gq1', '288.gu1', '432.jn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 93405312000, 36933, 87222233890, 87100665], 'label': '6912.ia.144.of1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '144.of1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.of1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565724
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.og1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mx1', '72.gn1', '72.pb1'], 'contains': ['288.fz1', '288.gs1', '288.gt1', '432.jo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185944609, 93405312000, 43942690, 36933, 87100665], 'label': '6912.ia.144.og1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '144.og1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.og1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565725
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ex1', '72.md1', '72.fw1', '72.gr1', '72.of1', '72.ol1', '72.on1', '72.pr1'], 'contains': ['288.d1', '432.jm1', '576.bi1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 32929, 87218571626, 36933, 2676], 'label': '6912.ia.144.oh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.oh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565726
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ex1', '72.fx1', '72.gs1', '72.og1'], 'contains': ['288.hh1', '432.jm1', '576.bj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 32929, 87218571626, 36933, 93405314676], 'label': '6912.ia.144.oi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '144.oi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565727
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ok1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ez1', '72.nb1', '72.gt1', '72.nw1', '72.oc1', '72.pc1', '72.pi1', '72.pt1'], 'contains': ['288.ga1', '288.gf1', '288.gm1', '432.jq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 7654690, 36933], 'label': '6912.ia.144.ok1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.oj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ok1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565728
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.my1', '72.ha1', '72.nv1', '72.ob1', '72.pc1', '72.ph1', '72.ps1'], 'contains': ['288.ga1', '288.ge1', '288.go1', '432.jp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.144.oj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ok1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oj1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565729
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '6.o1', '9.a1'], 'contains': ['36.d1', '36.h1', '36.gj1', '36.bn1', '36.cs1', '36.he1', '36.ib1', '54.s1', '72.ir1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.y1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565730
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ol1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.fa1', '72.mz1', '72.gu1', '72.ny1', '72.ob1', '72.pe1', '72.pi1', '72.pu1'], 'contains': ['288.ga1', '288.gg1', '288.gl1', '432.jr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83495329, 87261789839], 'label': '6912.ia.144.ol1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.ol1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ol1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565731
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.om1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.na1', '72.gu1', '72.nv1', '72.oe1', '72.pd1', '72.pj1', '72.pt1'], 'contains': ['288.ga1', '288.gg1', '288.gn1', '432.js1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87185912426, 83495329], 'label': '6912.ia.144.om1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.om1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.om1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565732
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.on1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.my1', '72.gt1', '72.nx1', '72.od1', '72.pf1', '72.pj1', '72.pu1'], 'contains': ['288.ga1', '288.gh1', '288.gm1', '432.jt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933, 87265415329], 'label': '6912.ia.144.on1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.on1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.on1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565733
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.fb1', '72.mz1', '72.gx1', '72.nw1', '72.od1', '72.pd1', '72.pk1', '72.ps1'], 'contains': ['288.ga1', '288.gi1', '288.gj1', '432.ju1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87261789839, 87261786529], 'label': '6912.ia.144.oo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.oo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oo1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565734
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.op1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.na1', '72.gx1', '72.nx1', '72.oc1', '72.pe1', '72.ph1', '72.pv1'], 'contains': ['288.ga1', '288.gi1', '288.gk1', '432.jv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87185912426, 87261786529], 'label': '6912.ia.144.op1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.op1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.op1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565735
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ey1', '48.fc1', '48.fd1', '72.nb1', '72.ha1', '72.ny1', '72.oe1', '72.pf1', '72.pk1', '72.pv1'], 'contains': ['288.c1', '288.ga1', '288.go1', '432.jw1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 87185912426], 'label': '6912.ia.144.oq1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '144.oq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565736
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.or1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nc1', '72.gw1', '72.pg1'], 'contains': ['288.gb1', '288.gr1', '288.gt1', '432.jx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 43942690, 36933, 87305695009, 87100665], 'label': '6912.ia.144.or1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '144.or1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.or1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565737
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.os1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.fe1', '72.nc1', '72.gz1', '72.pg1'], 'contains': ['288.gb1', '288.gu1', '288.gv1', '432.jy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 40297548, 36933, 87100665, 87261754346], 'label': '6912.ia.144.os1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '144.os1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.os1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565738
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ot1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ey1', '48.ff1', '48.fg1', '72.me1', '72.hb1', '72.nz1', '72.of1', '72.oo1', '72.po1', '72.pp1'], 'contains': ['288.d1', '432.jw1', '576.bl1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 32929, 36933, 87185912426, 2676], 'label': '6912.ia.144.ot1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.ot1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ot1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565739
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ou1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jn1', '48.ez1', '72.mg1', '72.oj1', '72.pl1'], 'contains': ['288.gc1', '288.gy1', '288.hd1', '432.jq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178324129, 7654690, 47537280, 36933], 'label': '6912.ia.144.ou1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ou1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ou1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565740
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '9.b1'], 'contains': ['36.ge1', '36.gf1', '36.gg1', '36.gh1', '36.gi1', '36.hg1', '36.hh1', '36.hi1', '36.hm1', '36.hp1', '36.ic1', '54.q1', '72.lx1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.18.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.z1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243565741
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ov1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jo1', '48.fa1', '72.mf1', '72.ok1', '72.pl1'], 'contains': ['288.gc1', '288.gz1', '288.hc1', '432.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83495329, 87261789839], 'label': '6912.ia.144.ov1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ov1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ov1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565742
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ow1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jp1', '48.fb1', '72.mf1', '72.oj1', '72.pm1'], 'contains': ['288.gc1', '288.ha1', '288.hb1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 79870533, 36933, 87261789839, 87261786529], 'label': '6912.ia.144.ow1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ow1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ow1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565743
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ox1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jq1', '48.fc1', '48.ff1', '48.fh1', '72.mg1', '72.ok1', '72.pm1'], 'contains': ['288.gc1', '288.he1', '288.hf1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.144.ox1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '144.ox1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ox1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565744
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ey1', '48.fh1', '48.fi1', '72.hc1', '72.oa1', '72.og1'], 'contains': ['288.hh1', '432.jw1', '576.bn1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 32929, 36933, 87185912426, 93405314676], 'label': '6912.ia.144.oy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1', 'old_label': '144.oy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565745
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.oz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.js1', '48.fb1', '72.pn1'], 'contains': ['288.gd1', '288.hi1', '288.hj1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 93485182533, 36933, 87261789839, 87261786529], 'label': '6912.ia.144.oz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '144.oz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.oz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565746
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jt1', '48.fc1', '48.fg1', '48.fi1', '72.pn1'], 'contains': ['288.gd1', '288.hk1', '288.hl1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 32929, 93452849280, 36933, 87185912426], 'label': '6912.ia.144.pa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '144.pa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pa1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243565749
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jv1', '48.fd1', '48.fg1', '48.fh1', '48.fi1'], 'contains': ['288.ho1', '432.jw1', '576.bq1'], 'core': '864.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [9465, 93525428474, 32929, 36933, 87185912426], 'label': '6912.ia.144.pd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.pd1', 'old_label': '144.pd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565750
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.jv1', '48.fe1'], 'contains': ['288.hp1', '432.jy1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40297548, 36933, 87100665, 93448860794, 87261754346], 'label': '6912.ia.144.pe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.pe1', 'old_label': '144.pe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pe1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565751
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '9.b1'], 'contains': ['36.gf1', '36.gl1', '36.gm1', '36.hk1', '36.hl1', '36.ij1', '36.ik1', '54.r1', '72.ly1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 87178291200, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.18.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ba1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565752
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fk1', '72.ir1', '72.qg1'], 'contains': ['288.iq1', '288.jh1', '288.jl1', '288.it1', '288.ix1', '288.kb1', '288.ko1', '432.kb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 40316613, 87178291200, 2676, 127407813], 'label': '6912.ia.144.pi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565753
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fl1', '72.iu1', '72.qg1'], 'contains': ['288.iq1', '288.ji1', '288.jj1', '288.hr1', '288.hs1', '288.iw1', '288.ja1', '288.kn1', '288.kp1', '288.ie1', '288.if1', '432.kc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 127370880, 40280426, 87178291200, 2676], 'label': '6912.ia.144.pj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565754
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fm1', '72.iv1', '72.qg1'], 'contains': ['288.iq1', '288.jk1', '288.jm1', '288.jd1', '288.jf1', '288.kq1', '288.kr1', '432.kd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 43909226, 87178291200, 2676, 127407813], 'label': '6912.ia.144.pk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.ph1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565755
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.px1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.fu1', '72.d1', '72.qg1', '72.qi1'], 'contains': ['288.jh1', '288.ji1', '288.jk1', '288.jq1', '288.jr1', '288.ke1', '288.ki1', '288.la1', '288.le1', '288.mx1', '288.my1', '432.ki1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.144.px1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.px1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565756
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.py1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.fv1', '72.e1', '72.qg1', '72.qi1'], 'contains': ['288.jh1', '288.jj1', '288.jm1', '288.kg1', '288.kl1', '288.ld1', '288.lf1', '432.kj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 43909226, 87178328133, 2676, 87091200], 'label': '6912.ia.144.py1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.py1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565757
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.fw1', '72.f1', '72.qg1', '72.qi1'], 'contains': ['288.ji1', '288.jl1', '288.jm1', '288.lb1', '288.lc1', '288.lp1', '288.lq1', '432.kk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [43909226, 43908480, 87178328133, 2676, 87091200], 'label': '6912.ia.144.pz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565758
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.fx1', '72.g1', '72.qg1', '72.qi1'], 'contains': ['288.jj1', '288.jk1', '288.jl1', '288.ll1', '288.lm1', '288.lt1', '288.lv1', '432.kl1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [43908480, 24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.144.qa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qa1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565759
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fr1', '48.fy1', '72.ir1', '72.qi1'], 'contains': ['288.jh1', '288.jl1', '288.jn1', '288.kb1', '288.ko1', '288.ly1', '288.me1', '432.km1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 127370880, 87178328133, 2676, 40279680], 'label': '6912.ia.144.qb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565760
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.g1', '48.fr1', '72.is1', '72.qj1'], 'contains': ['288.f1', '288.jo1', '288.mg1', '432.km1', '576.di1'], 'core': '288.f1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87178291200, 7657413, 47537280, 40279680], 'label': '6912.ia.144.qc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.pn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565761
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fs1', '48.fz1', '72.it1', '72.qj1'], 'contains': ['288.jo1', '288.mb1', '288.mi1', '432.kn1', '576.dj1'], 'core': '576.c1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 47537280, 87178328133, 40315919, 40279680], 'label': '6912.ia.144.qd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '144.po1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565762
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.l1', '9.b1'], 'contains': ['36.b1', '36.gf1', '36.gk1', '36.gn1', '36.hj1', '36.ii1', '36.il1', '54.s1', '72.lz1'], 'core': '36.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.bb1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bb1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243565763
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fs1', '48.ga1', '72.iu1', '72.qi1'], 'contains': ['288.ji1', '288.jj1', '288.jn1', '288.kn1', '288.kp1', '288.md1', '288.mk1', '432.kn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 40280426, 87178328133, 2676, 40279680], 'label': '6912.ia.144.qe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '144.pp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qe1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565764
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ft1', '48.gb1', '72.iv1', '72.qi1'], 'contains': ['288.jk1', '288.jm1', '288.jn1', '288.kq1', '288.kr1', '288.mn1', '288.mr1', '432.ko1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 43909226, 87178328133, 2676, 40279680], 'label': '6912.ia.144.qf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.pq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565765
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ft1', '48.gc1', '72.iw1', '72.qj1'], 'contains': ['288.jo1', '288.mo1', '288.ms1', '432.ko1', '576.dn1'], 'core': '576.c1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 47537280, 43944719, 87178328133, 40279680], 'label': '6912.ia.144.qg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '144.pr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565766
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ft1', '48.gd1', '72.ix1'], 'contains': ['288.jp1', '288.mp1', '288.mv1', '432.ko1', '576.do1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 87178328133, 40279680], 'label': '6912.ia.144.qh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ix1', 'old_label': '144.ps1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565767
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fj1', '72.d1'], 'contains': ['288.hq1', '288.hr1', '288.ht1', '288.jq1', '288.jr1', '288.ia1', '288.ic1', '288.ij1', '288.ik1', '288.mx1', '288.my1', '432.jz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87178291200, 7657413, 24536, 87128133, 83476887], 'label': '6912.ia.144.pf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '144.pt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566664
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '128.c1', '192.h1', '192.ce1', '192.dj1', '192.dl1'], 'contains': ['768.b1', '1152.r1', '1152.u1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405312000, 7657413, 47537280], 'label': '6912.ia.384.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '384.o1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565768
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fk1', '72.ja1', '72.qh1'], 'contains': ['288.ir1', '288.jt1', '288.jx1', '288.is1', '288.iy1', '288.kc1', '288.kt1', '432.kb1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 40316613, 93405312000, 87178291200, 127407813], 'label': '6912.ia.144.pl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.pu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565769
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fl1', '72.jb1', '72.qh1'], 'contains': ['288.ir1', '288.ju1', '288.jv1', '288.hv1', '288.hw1', '288.iv1', '288.iz1', '288.ks1', '288.ku1', '288.ig1', '288.ih1', '432.kc1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 87178291200, 40315919], 'label': '6912.ia.144.pm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.pv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565770
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fm1', '72.jc1', '72.qh1'], 'contains': ['288.ir1', '288.jw1', '288.jy1', '288.jc1', '288.je1', '288.kv1', '288.kw1', '432.kd1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200, 43944719, 127407813], 'label': '6912.ia.144.pn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.pw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565771
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fu1', '72.i1', '72.qh1', '72.qk1'], 'contains': ['288.jt1', '288.ju1', '288.jw1', '288.jz1', '288.ka1', '288.kd1', '288.kh1', '288.kx1', '288.lh1', '288.mz1', '288.na1', '432.ki1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 83476887, 87178328133, 87091200], 'label': '6912.ia.144.qi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.px1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565772
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fv1', '72.j1', '72.qh1', '72.qk1'], 'contains': ['288.jt1', '288.jv1', '288.jy1', '288.kf1', '288.kk1', '288.lg1', '288.li1', '432.kj1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 43944719, 87178328133, 87091200], 'label': '6912.ia.144.qj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.py1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565773
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '9.b1'], 'contains': ['36.gh1', '36.gk1', '36.gm1', '36.hw1', '36.hx1', '36.ip1', '36.iq1', '54.t1', '72.ma1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87178291200, 47537280, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.18.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bc1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243565774
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fw1', '72.n1', '72.qh1', '72.qk1'], 'contains': ['288.ju1', '288.jx1', '288.jy1', '288.ky1', '288.kz1', '288.ln1', '288.lo1', '432.kk1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 43945413, 43944719, 87178328133, 87091200], 'label': '6912.ia.144.qk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.pz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565775
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ql1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fx1', '72.r1', '72.qh1', '72.qk1'], 'contains': ['288.jv1', '288.jw1', '288.jx1', '288.lj1', '288.lk1', '288.ls1', '288.lu1', '432.kl1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 43945413, 83476887, 87178328133, 87091200], 'label': '6912.ia.144.ql1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qa1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ql1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565776
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.g1', '48.fy1', '72.ja1', '72.qk1'], 'contains': ['288.e1', '288.jt1', '288.jx1', '288.kc1', '288.kt1', '288.lx1', '288.mf1', '432.km1'], 'core': '288.e1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87178328133, 40279680], 'label': '6912.ia.144.qm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.qb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565777
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fz1', '48.ga1', '72.jb1', '72.qk1'], 'contains': ['288.e1', '288.ju1', '288.jv1', '288.ks1', '288.ku1', '288.ma1', '288.mj1', '432.kn1'], 'core': '288.e1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 87178328133, 40315919, 40279680], 'label': '6912.ia.144.qn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '144.qc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565778
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gb1', '48.gc1', '48.gd1', '72.jc1', '72.qk1'], 'contains': ['288.e1', '288.jw1', '288.jy1', '288.kv1', '288.kw1', '288.mm1', '288.mq1', '432.ko1'], 'core': '288.e1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 93405312000, 43944719, 87178328133, 40279680], 'label': '6912.ia.144.qo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565779
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fj1', '72.i1'], 'contains': ['288.hu1', '288.hv1', '288.hx1', '288.jz1', '288.ka1', '288.hz1', '288.ib1', '288.ii1', '288.il1', '288.mz1', '288.na1', '432.jz1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 87128133, 83476887], 'label': '6912.ia.144.pg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '144.qe1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565780
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ph1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.s1'], 'contains': ['288.hw1', '288.hx1', '288.hy1', '288.im1', '288.in1', '288.io1', '288.ip1', '432.ka1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [119759865, 93405312000, 87128133, 83476887, 87178328133], 'label': '6912.ia.144.ph1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '144.qf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ph1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565781
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.po1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fn1', '72.jf1', '72.qh1'], 'contains': ['288.is1', '288.iv1', '288.jc1', '288.kd1', '288.kf1', '288.ky1', '288.lj1', '432.ke1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 7657413, 43944719, 127407813], 'label': '6912.ia.144.po1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.po1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565782
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fn1', '72.jg1', '72.qg1'], 'contains': ['288.it1', '288.iw1', '288.jd1', '288.ke1', '288.kg1', '288.lb1', '288.ll1', '432.ke1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 43909226, 7657413, 2676, 127407813], 'label': '6912.ia.144.pp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.qh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565783
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fo1', '72.jh1', '72.qh1'], 'contains': ['288.is1', '288.iz1', '288.je1', '288.kh1', '288.kk1', '288.ln1', '288.lu1', '432.kf1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 7657413, 87222235919, 127407813], 'label': '6912.ia.144.pq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565784
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['1152.bm1', '1152.bt1', '1152.bv1', '1152.bo1', '1152.bx1', '1152.by1', '1152.ba1', '1152.bg1', '1152.bj1', '1152.bq1', '1152.bk1', '1152.br1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.c1'], 'contains': ['12.b1', '12.c1', '12.g1', '12.bp1', '12.bt1', '12.cb1', '12.cq1', '18.bb1', '18.bl1', '24.dg1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.b1', '12.c1', '12.g1', '24.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243565785
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '6.s1', '9.b1'], 'contains': ['36.gh1', '36.gl1', '36.gn1', '36.hv1', '36.hy1', '36.io1', '36.ir1', '54.u1', '72.mb1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.bd1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bd1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243565786
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fo1', '72.ji1', '72.qg1'], 'contains': ['288.it1', '288.ja1', '288.jf1', '288.ki1', '288.kl1', '288.lp1', '288.lv1', '432.kf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 40316613, 87222200426, 2676, 127407813], 'label': '6912.ia.144.pr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565787
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ps1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fo1', '72.jj1'], 'contains': ['288.iu1', '288.jb1', '288.jg1', '288.kj1', '288.km1', '288.lr1', '288.lw1', '432.kf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 40316613, 87222200426, 93405314676, 127407813], 'label': '6912.ia.144.ps1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.qk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ps1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565788
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fp1', '72.jq1', '72.qh1'], 'contains': ['288.iv1', '288.iy1', '288.je1', '288.kx1', '288.kz1', '288.lg1', '288.lk1', '432.kg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87185948613, 87222235919, 127407813], 'label': '6912.ia.144.pt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.ql1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565789
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fp1', '72.kd1', '72.qg1'], 'contains': ['288.iw1', '288.ix1', '288.jf1', '288.la1', '288.lc1', '288.ld1', '288.lm1', '432.kg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87185911680, 87222200426, 2676, 127407813], 'label': '6912.ia.144.pu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565790
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fq1', '72.ke1', '72.qg1'], 'contains': ['288.ix1', '288.ja1', '288.jd1', '288.le1', '288.lf1', '288.lq1', '288.lt1', '432.kh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87185911680, 43909226, 2676, 127407813], 'label': '6912.ia.144.pv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565791
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.pw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fq1', '72.kg1', '72.qh1'], 'contains': ['288.iy1', '288.iz1', '288.jc1', '288.lh1', '288.li1', '288.lo1', '288.ls1', '432.kh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87185948613, 43944719, 127407813], 'label': '6912.ia.144.pw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.pw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565792
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.ge1', '72.bj1', '72.qg1', '72.qi1'], 'contains': ['288.kb1', '288.ke1', '288.kl1', '288.kn1', '288.kq1', '288.lc1', '288.lt1', '432.kp1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87218607813, 24536, 87091200, 83468087], 'label': '6912.ia.144.qp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565793
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.gf1', '72.bk1', '72.qg1', '72.qi1'], 'contains': ['288.kb1', '288.kg1', '288.ki1', '288.kp1', '288.kr1', '288.lm1', '288.lq1', '432.kq1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87218607813, 43909226, 2676, 87091200], 'label': '6912.ia.144.qq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565794
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ge1', '72.bl1', '72.qh1', '72.qk1'], 'contains': ['288.kc1', '288.kd1', '288.kk1', '288.ks1', '288.kv1', '288.kz1', '288.ls1', '432.kp1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 93405312000, 7657413, 83476887, 87091200], 'label': '6912.ia.144.qr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565795
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gf1', '72.bm1', '72.qh1', '72.qk1'], 'contains': ['288.kc1', '288.kf1', '288.kh1', '288.ku1', '288.kw1', '288.lk1', '288.lo1', '432.kq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 87218607813, 93405312000, 43944719, 87091200], 'label': '6912.ia.144.qs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565796
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.m1', '9.a1'], 'contains': ['36.c1', '36.e1', '36.f1', '36.gj1', '36.cr1', '36.ct1', '36.iw1', '54.u1', '72.iu1'], 'core': '36.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.be1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.be1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565797
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.gg1', '72.ck1', '72.qg1', '72.qi1'], 'contains': ['288.kn1', '288.ko1', '288.kr1', '288.la1', '288.lb1', '288.lf1', '288.lv1', '432.kr1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87218607813, 43909226, 43908480, 2676, 87091200], 'label': '6912.ia.144.qt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565798
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.gh1', '72.cl1', '72.qg1', '72.qi1'], 'contains': ['288.ko1', '288.kp1', '288.kq1', '288.ld1', '288.le1', '288.ll1', '288.lp1', '432.ks1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87218607813, 43908480, 24536, 87091200, 83468087], 'label': '6912.ia.144.qu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.qu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565799
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gg1', '72.cn1', '72.qh1', '72.qk1'], 'contains': ['288.ks1', '288.kt1', '288.kw1', '288.kx1', '288.ky1', '288.li1', '288.lu1', '432.kr1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 93405312000, 43945413, 43944719, 87091200], 'label': '6912.ia.144.qv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565800
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gh1', '72.cs1', '72.qh1', '72.qk1'], 'contains': ['288.kt1', '288.ku1', '288.kv1', '288.lg1', '288.lh1', '288.lj1', '288.ln1', '432.ks1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 93405312000, 43945413, 83476887, 87091200], 'label': '6912.ia.144.qw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565801
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gi1', '48.gk1', '72.jf1', '72.qk1'], 'contains': ['288.kd1', '288.kf1', '288.ky1', '288.lj1', '288.lx1', '288.ma1', '288.mm1', '432.kt1'], 'core': '576.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 7657413, 40279680], 'label': '6912.ia.144.qx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565802
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gi1', '48.gl1', '72.jg1', '72.qi1'], 'contains': ['288.ke1', '288.kg1', '288.lb1', '288.ll1', '288.ly1', '288.md1', '288.mn1', '432.kt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 127370880, 43944719, 2676, 40279680], 'label': '6912.ia.144.qy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.qy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565803
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.qz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gj1', '48.gm1', '72.jh1', '72.qk1'], 'contains': ['288.kh1', '288.kk1', '288.ln1', '288.lu1', '288.lx1', '288.mj1', '288.mq1', '432.ku1'], 'core': '576.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 87222200426, 40279680], 'label': '6912.ia.144.qz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.qz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.qz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565804
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ra1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gj1', '48.gn1', '72.ji1', '72.qi1'], 'contains': ['288.ki1', '288.kl1', '288.lp1', '288.lv1', '288.ly1', '288.mk1', '288.mr1', '432.ku1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 127370880, 87222235919, 2676, 40279680], 'label': '6912.ia.144.ra1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.ra1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ra1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565805
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gj1', '48.go1', '72.jj1'], 'contains': ['288.kj1', '288.km1', '288.lr1', '288.lw1', '288.lz1', '288.ml1', '288.mt1', '432.ku1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 127370880, 87222235919, 93405314676, 40279680], 'label': '6912.ia.144.rb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '144.rb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565806
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gk1', '48.gl1', '72.jm1', '72.qj1'], 'contains': ['288.f1', '288.mb1', '288.mo1', '432.kt1', '576.fr1'], 'core': '288.f1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 43909226, 7657413, 47537280, 40279680], 'label': '6912.ia.144.rc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '144.rc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565807
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '6.t1', '9.a1'], 'contains': ['36.g1', '36.i1', '36.gj1', '36.cu1', '36.cv1', '36.jc1', '36.jm1', '54.w1', '72.iv1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.bf1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bf1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243565808
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gm1', '48.gn1', '48.go1', '72.jn1', '72.qj1'], 'contains': ['288.f1', '288.mi1', '288.ms1', '432.ku1', '576.fs1'], 'core': '288.f1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 7657413, 87222200426, 47537280, 40279680], 'label': '6912.ia.144.rd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '144.rd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565809
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.re1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gp1', '48.gq1', '72.jq1', '72.qk1'], 'contains': ['288.kx1', '288.kz1', '288.lg1', '288.lk1', '288.ma1', '288.mf1', '288.mq1', '432.kv1'], 'core': '576.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 87185948613, 40279680], 'label': '6912.ia.144.re1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.re1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.re1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565810
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gp1', '48.gr1', '72.jr1', '72.qj1'], 'contains': ['288.mb1', '288.mg1', '288.ms1', '432.kv1', '576.gc1'], 'core': '576.c1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 87222200426, 47537280, 87185948613, 40279680], 'label': '6912.ia.144.rf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '144.rf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565811
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gp1', '48.gs1', '72.js1'], 'contains': ['288.mc1', '288.mh1', '288.mu1', '432.kv1', '576.gd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 87222200426, 87185948613, 93452849280, 40279680], 'label': '6912.ia.144.rg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.js1', 'old_label': '144.rg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565812
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gq1', '48.gr1', '48.gs1', '72.kd1', '72.qi1'], 'contains': ['288.la1', '288.lc1', '288.ld1', '288.lm1', '288.md1', '288.me1', '288.mr1', '432.kv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 87185911680, 87222235919, 2676, 40279680], 'label': '6912.ia.144.rh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.rh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565813
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.ri1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gt1', '48.gu1', '72.ke1', '72.qi1'], 'contains': ['288.le1', '288.lf1', '288.lq1', '288.lt1', '288.me1', '288.mk1', '288.mn1', '432.kw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 87185911680, 43944719, 2676, 40279680], 'label': '6912.ia.144.ri1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '144.ri1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ri1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565814
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gt1', '48.gv1', '72.kf1', '72.qj1'], 'contains': ['288.mg1', '288.mi1', '288.mo1', '432.kw1', '576.gj1'], 'core': '576.c1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 43909226, 47537280, 87185948613, 40279680], 'label': '6912.ia.144.rj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '144.rj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565815
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '144.rk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gu1', '48.gv1', '72.kg1', '72.qk1'], 'contains': ['288.lh1', '288.li1', '288.lo1', '288.ls1', '288.mf1', '288.mj1', '288.mm1', '432.kw1'], 'core': '576.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 87185948613, 40279680], 'label': '6912.ia.144.rk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '144.rk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.rk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565816
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': ['36.jx1', '36.ke1', '36.kd1', '36.jw1'], 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.a1', '96.c1', '96.d1', '96.e1', '96.fp1', '96.fw1', '96.gb1', '96.gf1'], 'contains': ['576.b1', '576.c1', '576.fc1', '768.b1'], 'core': '192.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 40279680], 'label': '6912.ia.192.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': ['96.a1', '96.c1', '96.d1', '96.e1'], 'normal_contains': ['576.b1', '576.c1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '6912.ia', 'quotient_action_image': '8.5', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565817
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1', '48.cr1', '64.a1', '96.z1', '96.ba1', '96.bb1'], 'contains': ['384.d1', '384.i1', '576.g1', '576.h1', '576.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 87178291200, 47537280, 36933], 'label': '6912.ia.192.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565818
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '9.b1'], 'contains': ['36.gi1', '36.gk1', '36.gl1', '36.je1', '36.jf1', '36.jo1', '36.jp1', '54.v1', '72.mf1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 87178291200, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.18.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bg1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243565819
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '64.a1', '96.f1', '96.bc1', '96.bf1', '96.bg1', '96.bh1'], 'contains': ['384.a1', '384.j1', '576.a1', '576.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 2676], 'label': '6912.ia.192.d1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565820
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '64.a1', '96.bd1', '96.be1', '96.bi1', '96.bk1', '96.bl1'], 'contains': ['384.b1', '384.k1', '576.a1', '576.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 87178291200, 47537280, 36933], 'label': '6912.ia.192.e1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '192.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565821
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1', '48.dd1', '48.de1', '64.a1', '96.bj1'], 'contains': ['384.c1', '384.l1', '576.a1', '576.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120116474, 93405312000, 87178291200, 36933], 'label': '6912.ia.192.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '192.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565822
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '96.f1', '96.g1', '96.h1', '96.i1', '96.j1', '96.k1', '96.l1', '96.m1', '96.n1', '96.o1', '96.p1', '96.q1', '96.r1', '96.s1', '96.t1'], 'contains': ['384.a1', '384.m1', '384.h1', '576.d1', '576.e1', '576.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 36933, 2676, 40279680], 'label': '6912.ia.192.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565823
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dh1', '64.b1', '96.bc1', '96.g1', '96.bm1', '96.bn1', '96.bo1', '96.bp1', '96.bq1'], 'contains': ['384.a1', '384.n1', '576.j1', '576.k1', '576.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 2676], 'label': '6912.ia.192.g1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565824
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '64.b1', '96.bd1', '96.br1', '96.bt1', '96.bw1', '96.bx1'], 'contains': ['384.b1', '384.o1', '576.j1', '576.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 36933], 'label': '6912.ia.192.h1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '192.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565825
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1', '48.dp1', '64.b1', '96.z1', '96.bs1', '96.bu1'], 'contains': ['384.d1', '384.p1', '576.k1', '576.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 47537280, 36933], 'label': '6912.ia.192.i1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '192.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565826
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1', '48.dq1', '64.b1', '96.bv1'], 'contains': ['384.f1', '384.q1', '576.l1', '576.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [7620480, 93525427956, 47537280, 36933], 'label': '6912.ia.192.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '192.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565827
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dr1', '96.f1', '96.h1', '96.bm1', '96.by1', '96.bz1', '96.ca1', '96.cb1'], 'contains': ['384.a1', '384.r1', '576.n1', '576.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 2676], 'label': '6912.ia.192.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565828
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '64.c1', '96.be1', '96.br1', '96.cc1', '96.cd1', '96.ce1', '96.cf1', '96.cg1'], 'contains': ['384.b1', '384.s1', '576.p1', '576.q1', '576.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 36933, 746], 'label': '6912.ia.192.l1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '192.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565829
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '6.v1', '9.b1'], 'contains': ['36.gi1', '36.gm1', '36.gn1', '36.jd1', '36.jg1', '36.jn1', '36.jq1', '54.w1', '72.mg1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.bh1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bh1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243565830
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '64.c1', '96.bf1', '96.i1', '96.bn1', '96.by1', '96.ch1'], 'contains': ['384.a1', '384.t1', '576.p1', '576.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 36933, 746, 2676], 'label': '6912.ia.192.m1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565831
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1', '48.dy1', '64.c1', '96.ba1', '96.bs1', '96.ci1'], 'contains': ['384.d1', '384.u1', '576.q1', '576.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 47537280, 36933, 746], 'label': '6912.ia.192.n1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '192.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565832
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1', '48.dz1', '64.c1', '96.cj1'], 'contains': ['384.e1', '384.v1', '576.r1', '576.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [174404119680, 93525427956, 36933, 746], 'label': '6912.ia.192.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '192.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565833
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ea1', '64.d1', '96.bc1', '96.j1', '96.bm1', '96.ch1', '96.ck1', '96.cm1', '96.cn1'], 'contains': ['384.a1', '384.w1', '576.t1', '576.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 2676], 'label': '6912.ia.192.p1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565834
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1', '48.eb1', '64.d1', '96.z1', '96.ci1', '96.cl1'], 'contains': ['384.d1', '384.x1', '576.t1', '576.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 87185911680, 47537280, 36933], 'label': '6912.ia.192.q1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565835
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1', '48.ec1', '64.d1', '96.cj1'], 'contains': ['384.e1', '384.y1', '576.t1', '576.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [174404119680, 93525427956, 87185911680, 36933], 'label': '6912.ia.192.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '192.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565836
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '64.d1', '96.bd1', '96.cc1', '96.co1', '96.cp1', '96.cq1'], 'contains': ['384.b1', '384.z1', '576.u1', '576.v1', '576.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [87185911680, 93405312000, 47537280, 36933], 'label': '6912.ia.192.s1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '192.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565837
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ei1', '96.bg1', '96.i1', '96.k1', '96.bo1', '96.bz1', '96.ca1', '96.ck1'], 'contains': ['384.a1', '384.ba1', '576.x1', '576.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 2676], 'label': '6912.ia.192.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565838
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1', '64.e1', '96.be1', '96.bt1', '96.cd1', '96.co1', '96.cr1', '96.cs1', '96.ct1'], 'contains': ['384.b1', '384.bb1', '576.z1', '576.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 36933, 87178291946], 'label': '6912.ia.192.u1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '192.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565839
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1', '48.en1', '64.e1', '96.ba1', '96.bu1', '96.cl1'], 'contains': ['384.d1', '384.bc1', '576.z1', '576.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 47537280, 36933, 87178291946], 'label': '6912.ia.192.v1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565840
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '6.w1'], 'contains': ['36.go1', '36.jh1', '36.ju1', '54.w1', '72.ix1', '72.mh1', '72.mi1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 43909226, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.18.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bi1', 'old_label': '18.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bi1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 243565841
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1', '48.eo1', '64.e1', '96.bv1'], 'contains': ['384.f1', '384.bd1', '576.z1', '576.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93525427956, 47537280, 36933, 87178291946], 'label': '6912.ia.192.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '192.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565842
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '64.e1', '96.bf1', '96.l1', '96.bp1', '96.bz1', '96.cm1'], 'contains': ['384.a1', '384.be1', '576.ba1', '576.bb1', '576.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 36933, 2676, 87178291946], 'label': '6912.ia.192.x1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.x1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565843
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ep1', '64.f1', '96.bh1', '96.m1', '96.bn1', '96.bo1', '96.cb1', '96.cm1', '96.cn1'], 'contains': ['384.a1', '384.bf1', '576.bd1', '576.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 93405312000, 36933, 83468087], 'label': '6912.ia.192.y1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565844
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1', '64.f1', '96.bi1', '96.br1', '96.ce1', '96.co1', '96.cr1', '96.cu1', '96.cv1'], 'contains': ['384.b1', '384.bg1', '576.bd1', '576.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 79833600, 36933, 83468087], 'label': '6912.ia.192.z1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '192.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565845
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1', '48.eu1', '48.ev1', '64.f1', '96.bj1'], 'contains': ['384.c1', '384.bh1', '576.bd1', '576.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 43561327, 36933, 83468087], 'label': '6912.ia.192.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '192.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565846
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ce1', '48.ew1', '64.f1', '96.bb1', '96.bs1', '96.cl1'], 'contains': ['384.d1', '384.bi1', '576.be1', '576.bf1', '576.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [43576538, 79833600, 36933, 83468087], 'label': '6912.ia.192.bb1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '192.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565847
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ex1', '96.bg1', '96.l1', '96.n1', '96.bq1', '96.by1', '96.ca1', '96.cn1'], 'contains': ['384.a1', '384.bj1', '576.bh1', '576.bi1', '576.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87218571626, 36933, 2676], 'label': '6912.ia.192.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565848
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ey1', '64.g1', '96.bh1', '96.o1', '96.bp1', '96.bq1', '96.cb1', '96.ch1', '96.ck1'], 'contains': ['384.a1', '384.bk1', '576.bk1', '576.bl1', '576.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 93405312000, 36933, 87261759287], 'label': '6912.ia.192.bd1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565849
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '64.g1', '96.bi1', '96.bt1', '96.cc1', '96.cf1', '96.cs1', '96.cu1', '96.cw1'], 'contains': ['384.b1', '384.bl1', '576.bk1', '576.bm1', '576.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 79833600, 36933, 87261759287], 'label': '6912.ia.192.be1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '192.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.be1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565850
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1', '48.fd1', '48.fe1', '64.g1', '96.bj1'], 'contains': ['384.c1', '384.bm1', '576.bk1', '576.bp1', '576.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 43561327, 36933, 87261759287], 'label': '6912.ia.192.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '192.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565851
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.k1', '36.n1', '36.o1', '36.t1', '36.u1', '36.bc1', '36.bd1', '36.bw1', '36.bx1', '36.cg1', '36.ch1', '36.du1', '36.dv1', '36.eq1', '36.er1', '54.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565852
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1', '48.ff1', '64.g1', '96.bb1', '96.bu1', '96.ci1'], 'contains': ['384.d1', '384.bn1', '576.bl1', '576.bm1', '576.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43576538, 79833600, 36933, 87261759287], 'label': '6912.ia.192.bg1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565853
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1', '48.fg1', '64.g1', '96.cj1'], 'contains': ['384.e1', '384.bo1', '576.bl1', '576.bo1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [36933, 87261759287, 93448888538, 174436416000], 'label': '6912.ia.192.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '192.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565854
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1', '48.fh1', '64.g1', '96.bv1'], 'contains': ['384.f1', '384.bp1', '576.bm1', '576.bn1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [79833600, 36933, 87261759287, 93448888538], 'label': '6912.ia.192.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '192.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565855
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1', '48.fi1', '64.g1'], 'contains': ['384.g1', '384.bq1', '576.bn1', '576.bo1', '576.bp1', '576.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [43576538, 93485145600, 36933, 87261759287], 'label': '6912.ia.192.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.bj1', 'old_label': '192.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 243565856
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '96.bk1', '96.bw1', '96.cg1', '96.cp1', '96.ct1', '96.cv1', '96.cw1', '96.cx1', '96.cy1', '96.cz1', '96.da1', '96.db1', '96.dc1', '96.dd1', '96.de1'], 'contains': ['384.b1', '576.br1', '576.bx1', '576.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 47537280, 36933], 'label': '6912.ia.192.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '192.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565857
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1', '96.bk1', '96.bx1', '96.cd1', '96.cq1', '96.cu1', '96.cx1', '96.df1'], 'contains': ['384.b1', '576.bt1', '576.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178324129, 47537280, 36933], 'label': '6912.ia.192.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '192.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565858
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1', '96.bl1', '96.bw1', '96.ce1', '96.cq1', '96.cs1', '96.cy1', '96.df1'], 'contains': ['384.b1', '576.bu1', '576.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 79833600, 36933, 83495329], 'label': '6912.ia.192.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '192.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565859
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1', '96.bl1', '96.bx1', '96.cf1', '96.cp1', '96.cr1', '96.cz1', '96.df1'], 'contains': ['384.b1', '576.bw1', '576.ca1', '576.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 79833600, 36933, 87261786529], 'label': '6912.ia.192.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '192.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565860
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fr1', '64.h1', '96.z1', '96.ee1'], 'contains': ['384.i1', '384.p1', '384.x1', '576.dh1', '576.di1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [120115956, 7657413, 47537280, 87178328133], 'label': '6912.ia.192.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.bo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565861
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.fs1', '64.i1', '96.ba1', '96.ee1'], 'contains': ['384.i1', '384.u1', '384.bc1', '576.dj1', '576.dk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [120115956, 47537280, 746, 87178328133], 'label': '6912.ia.192.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.bp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565862
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.c1'], 'contains': ['36.k1', '36.m1', '36.p1', '36.s1', '36.v1', '36.bb1', '36.be1', '36.jz1', '36.ka1', '36.kb1', '36.kc1', '36.bv1', '36.by1', '36.cf1', '36.ci1', '36.dt1', '36.dw1', '36.ep1', '36.es1', '36.kf1', '36.kg1', '36.kh1', '36.ki1', '54.b1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565863
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ft1', '64.j1', '96.bb1', '96.ee1'], 'contains': ['384.i1', '384.bi1', '384.bn1', '576.dm1', '576.dn1', '576.do1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [43570136, 79833600, 87178328133, 83468087], 'label': '6912.ia.192.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.bq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565864
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '96.dw1', '96.ef1', '96.eg1', '96.eh1', '96.ei1', '96.ej1', '96.ek1', '96.el1'], 'contains': ['384.j1', '384.m1', '384.r1', '576.dg1', '576.dp1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178328133, 2676, 40279680], 'label': '6912.ia.192.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.br1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565865
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '96.dw1', '96.dm1', '96.dn1', '96.do1', '96.dp1'], 'contains': ['384.j1', '384.h1', '384.r1', '576.cd1', '576.ce1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200, 2676], 'label': '6912.ia.192.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.bs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565866
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.h1', '96.bc1', '96.ef1', '96.dm1', '96.en1', '96.eo1'], 'contains': ['384.j1', '384.n1', '384.w1', '576.dh1', '576.dq1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93405312000, 87178328133, 2676], 'label': '6912.ia.192.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.bt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565867
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.g1', '64.h1', '96.bd1', '96.ep1'], 'contains': ['384.k1', '384.o1', '384.z1', '576.di1', '576.dq1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 87178328133], 'label': '6912.ia.192.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '192.bu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ce1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565868
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.fz1', '64.i1', '96.be1', '96.ep1'], 'contains': ['384.k1', '384.s1', '384.bb1', '576.dj1', '576.dr1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [36239, 93405312000, 47537280, 87178328133], 'label': '6912.ia.192.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.bv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565869
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.i1', '96.bf1', '96.eg1', '96.dn1', '96.en1'], 'contains': ['384.j1', '384.t1', '384.be1', '576.dk1', '576.dr1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [93405312000, 746, 87178328133, 2676], 'label': '6912.ia.192.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.bw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565870
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bg1', '96.eg1', '96.eh1', '96.dn1', '96.do1', '96.eo1'], 'contains': ['384.j1', '384.ba1', '384.bj1', '576.dl1', '576.ds1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 40280426, 87178328133, 2676], 'label': '6912.ia.192.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.bx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565871
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.j1', '96.bh1', '96.ei1', '96.dp1', '96.en1', '96.eo1'], 'contains': ['384.j1', '384.bf1', '384.bk1', '576.dm1', '576.dt1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6851, 93405312000, 87178328133, 83468087], 'label': '6912.ia.192.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.by1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565872
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gc1', '64.j1', '96.bi1', '96.ep1'], 'contains': ['384.k1', '384.bg1', '384.bl1', '576.dn1', '576.dt1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 79833600, 83476887, 87178328133], 'label': '6912.ia.192.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.bz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565873
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.l1', '36.m1', '36.o1', '36.y1', '36.z1', '36.bj1', '36.bk1', '36.cb1', '36.cc1', '36.cm1', '36.cn1', '36.em1', '36.en1', '36.eu1', '36.ev1', '54.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 43909226, 93405312000, 87178291200, 40297548, 36933], 'label': '6912.ia.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565874
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gd1', '64.j1', '96.bj1'], 'contains': ['384.l1', '384.bh1', '384.bm1', '576.do1', '576.dt1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [93405312000, 43561327, 87178328133, 83468087], 'label': '6912.ia.192.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '192.ca1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565875
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1', '96.dw1', '96.dx1', '96.dy1', '96.dz1', '96.ea1', '96.eb1', '96.ec1'], 'contains': ['384.m1', '384.h1', '576.dd1', '576.de1', '576.df1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 2676], 'label': '6912.ia.192.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.by1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565876
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.g1', '96.ef1', '96.dx1', '96.eq1', '96.er1', '96.es1', '96.et1', '96.eu1', '96.fm1'], 'contains': ['384.m1', '384.n1', '576.du1', '576.dv1', '576.dw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 7657413, 2676, 87091200], 'label': '6912.ia.192.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565877
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '96.dw1', '96.el1', '96.eq1', '96.ev1', '96.ew1', '96.ex1', '96.ey1', '96.ez1'], 'contains': ['384.m1', '384.r1', '576.dx1', '576.dy1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 2676, 87305699013, 40279680], 'label': '6912.ia.192.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565878
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.eg1', '96.dy1', '96.er1', '96.ev1', '96.fa1', '96.fb1', '96.fc1', '96.fq1'], 'contains': ['384.m1', '384.t1', '384.ba1', '576.dz1', '576.ea1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 40315919, 2676, 40279680], 'label': '6912.ia.192.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.ce1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565879
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.j1', '96.ef1', '96.dz1', '96.ew1', '96.fa1', '96.fd1', '96.fe1', '96.ff1', '96.ft1'], 'contains': ['384.m1', '384.w1', '576.eb1', '576.ec1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87185948613, 2676, 87091200], 'label': '6912.ia.192.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.co1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565880
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.k1', '96.eh1', '96.dy1', '96.es1', '96.ex1', '96.fd1', '96.fg1', '96.fh1', '96.fq1'], 'contains': ['384.m1', '384.ba1', '576.ed1', '576.ee1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40304216, 93405312000, 87105687, 40279680], 'label': '6912.ia.192.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565881
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.l1', '96.eg1', '96.ea1', '96.et1', '96.ex1', '96.fe1', '96.fi1', '96.fj1', '96.fz1'], 'contains': ['384.m1', '384.be1', '384.bj1', '576.ef1', '576.eg1', '576.eh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87218571626, 2676, 40279680], 'label': '6912.ia.192.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.ch1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565902
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1', '96.do1', '96.dy1', '96.dt1'], 'contains': ['384.h1', '384.ba1', '576.co1', '576.cp1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 87105687, 40310618], 'label': '6912.ia.192.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '192.cz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565882
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.m1', '96.ei1', '96.eb1', '96.er1', '96.ey1', '96.fe1', '96.fg1', '96.fk1', '96.ga1'], 'contains': ['384.m1', '384.bf1', '576.ei1', '576.ej1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 24536, 83476887, 87091200], 'label': '6912.ia.192.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.ci1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565883
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.n1', '96.eh1', '96.ea1', '96.eu1', '96.ev1', '96.ff1', '96.fk1', '96.fl1', '96.fz1'], 'contains': ['384.m1', '384.bj1', '576.ek1', '576.el1', '576.em1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40304216, 93405312000, 87265396887, 40279680], 'label': '6912.ia.192.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565884
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.c1'], 'contains': ['36.l1', '36.n1', '36.p1', '36.x1', '36.ba1', '36.bi1', '36.bm1', '36.ca1', '36.cd1', '36.cl1', '36.co1', '36.el1', '36.eo1', '36.et1', '36.ew1', '54.d1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565885
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.o1', '96.ei1', '96.ec1', '96.et1', '96.ez1', '96.fa1', '96.fh1', '96.fl1', '96.ge1'], 'contains': ['384.m1', '384.bk1', '576.en1', '576.eo1', '576.ep1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87261768087, 24536, 87091200], 'label': '6912.ia.192.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.ck1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ct1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565886
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.p1', '96.ej1', '96.dx1', '96.ew1', '96.fb1', '96.fg1', '96.fi1', '96.fl1', '96.fm1'], 'contains': ['384.m1', '576.eq1', '576.eu1', '576.ey1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 43908480, 2676, 87091200], 'label': '6912.ia.192.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565887
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.q1', '96.ej1', '96.dz1', '96.eq1', '96.fc1', '96.fh1', '96.fj1', '96.fk1', '96.ft1'], 'contains': ['384.m1', '576.er1', '576.ev1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87222236613, 2676, 87091200], 'label': '6912.ia.192.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565888
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.r1', '96.ek1', '96.eb1', '96.es1', '96.ez1', '96.fb1', '96.ff1', '96.fj1', '96.ga1'], 'contains': ['384.m1', '576.es1', '576.ew1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 43944719, 2676, 87091200], 'label': '6912.ia.192.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565889
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.s1', '96.ek1', '96.ec1', '96.eu1', '96.ey1', '96.fc1', '96.fd1', '96.fi1', '96.ge1'], 'contains': ['384.m1', '576.et1', '576.ex1', '576.ez1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87222235919, 2676, 87091200], 'label': '6912.ia.192.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.co1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243565890
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.t1', '96.el1', '96.fm1', '96.fq1', '96.ft1', '96.fz1', '96.ga1', '96.ge1'], 'contains': ['384.m1', '576.b1', '576.fa1', '576.fb1'], 'core': '576.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 2676, 40279680], 'label': '6912.ia.192.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.cp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243565891
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.u1', '96.em1', '96.gc1', '96.gg1'], 'contains': ['576.b1', '576.fd1', '576.fe1', '768.c1'], 'core': '576.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 40279680], 'label': '6912.ia.192.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '192.cq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565892
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.v1', '96.ed1', '96.fn1', '96.fr1', '96.fu1', '96.fx1', '96.gd1', '96.gh1'], 'contains': ['576.c1', '576.fa1', '576.fd1', '768.d1'], 'core': '576.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 40279680], 'label': '6912.ia.192.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '192.cr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.da1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565893
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.w1', '96.fs1', '96.fv1', '96.gi1'], 'contains': ['576.fa1', '576.fc1', '576.fe1', '768.e1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40279680], 'label': '6912.ia.192.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1', 'old_label': '192.cs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.db1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565894
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.x1', '96.fo1', '96.fy1', '96.gj1'], 'contains': ['576.c1', '576.fb1', '576.fe1', '768.f1'], 'core': '576.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93525427956, 127370880, 47537280, 40279680], 'label': '6912.ia.192.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '192.ct1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243565895
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': ['1152.bn1', '1152.bu1', '1152.bw1', '1152.bo1', '1152.bx1', '1152.by1', '1152.u1', '1152.bd1', '1152.be1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.e1', '12.h1', '12.k1', '12.l1', '12.u1', '12.w1', '18.be1', '18.bn1', '24.bg1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '12.e1', '12.h1', '24.e1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243565896
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.r1', '36.s1', '36.u1', '36.bg1', '36.bh1', '36.bi1', '36.bk1', '36.dy1', '36.dz1', '36.eb1', '36.ec1', '36.fi1', '36.fj1', '36.fl1', '36.fm1', '54.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 93405312000, 43908480, 87178291200, 40297548, 36933], 'label': '6912.ia.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565897
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '96.y1', '96.gk1'], 'contains': ['576.fb1', '576.fc1', '576.fd1', '576.fe1', '768.g1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 127370880, 93452849280, 40279680], 'label': '6912.ia.192.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '192.cu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565898
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1', '96.dm1', '96.dq1', '96.dr1'], 'contains': ['384.h1', '384.n1', '576.cf1', '576.cg1', '576.ch1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 7657413, 87128133, 2676], 'label': '6912.ia.192.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.cv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565899
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '96.dw1', '96.ds1', '96.dt1'], 'contains': ['384.h1', '384.r1', '576.ci1', '576.cj1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 2676, 87305699013], 'label': '6912.ia.192.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '192.cw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565900
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.dn1', '96.dy1', '96.dq1', '96.ds1', '96.du1'], 'contains': ['384.h1', '384.t1', '384.ba1', '576.ck1', '576.cl1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 40280426, 2676], 'label': '6912.ia.192.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.cx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565903
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.l1', '96.dn1', '96.ea1', '96.dr1', '96.dt1', '96.dv1'], 'contains': ['384.h1', '384.be1', '384.bj1', '576.cq1', '576.cr1', '576.cs1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 87218571626, 2676], 'label': '6912.ia.192.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.da1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565904
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.m1', '96.dp1', '96.dq1', '96.dv1'], 'contains': ['384.h1', '384.bf1', '576.ct1', '576.cu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 24536, 87128133, 83476887], 'label': '6912.ia.192.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.db1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565905
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1', '96.do1', '96.ea1', '96.ds1'], 'contains': ['384.h1', '384.bj1', '576.cv1', '576.cw1', '576.cx1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405312000, 87265396887, 40310618], 'label': '6912.ia.192.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '192.dc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565906
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1', '96.dp1', '96.dr1', '96.du1'], 'contains': ['384.h1', '384.bk1', '576.cy1', '576.cz1', '576.da1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87261768087, 24536, 87128133], 'label': '6912.ia.192.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565907
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '9.c1'], 'contains': ['36.r1', '36.t1', '36.v1', '36.bf1', '36.bj1', '36.bl1', '36.bm1', '36.dx1', '36.ea1', '36.ed1', '36.ee1', '36.fh1', '36.fk1', '36.fn1', '36.fo1', '54.f1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 43908480, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.18.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243565908
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bm1', '96.ef1', '96.dm1', '96.gl1', '96.gm1'], 'contains': ['384.n1', '384.r1', '384.w1', '576.ff1', '576.fg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93405312000, 87265419333, 2676], 'label': '6912.ia.192.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.de1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565909
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.l1', '96.bn1', '96.en1', '96.er1', '96.dq1', '96.gl1'], 'contains': ['384.n1', '384.t1', '384.bf1', '576.fh1', '576.fi1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 2676], 'label': '6912.ia.192.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.df1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565910
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bo1', '96.eo1', '96.er1', '96.dq1', '96.gm1'], 'contains': ['384.n1', '384.ba1', '384.bf1', '576.fj1', '576.fk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 83476887], 'label': '6912.ia.192.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565911
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.m1', '96.bp1', '96.en1', '96.et1', '96.dr1', '96.gm1'], 'contains': ['384.n1', '384.be1', '384.bk1', '576.fl1', '576.fm1', '576.fn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 87185947919, 93405312000, 2676], 'label': '6912.ia.192.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565912
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bq1', '96.eo1', '96.et1', '96.dr1', '96.gl1'], 'contains': ['384.n1', '384.bj1', '384.bk1', '576.fo1', '576.fp1', '576.fq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 87261768087], 'label': '6912.ia.192.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.di1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565913
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gk1', '64.l1', '96.br1', '96.ep1'], 'contains': ['384.o1', '384.s1', '384.bg1', '576.fh1', '576.fr1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 7621226], 'label': '6912.ia.192.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.dj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565914
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gl1', '64.l1', '96.bs1', '96.ee1'], 'contains': ['384.p1', '384.u1', '384.bi1', '576.fi1', '576.fr1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [7620480, 7656719, 120115956, 47537280], 'label': '6912.ia.192.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '192.dk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565915
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gm1', '64.m1', '96.bt1', '96.ep1'], 'contains': ['384.o1', '384.bb1', '384.bl1', '576.fl1', '576.fs1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 7657413, 47537280, 87185912426], 'label': '6912.ia.192.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.dl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565916
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gn1', '64.m1', '96.bu1', '96.ee1'], 'contains': ['384.p1', '384.bc1', '384.bn1', '576.fm1', '576.fs1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7620480, 120115956, 87185947919, 47537280], 'label': '6912.ia.192.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.dm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565917
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.go1', '64.m1', '96.bv1'], 'contains': ['384.q1', '384.bd1', '384.bp1', '576.fn1', '576.fs1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [7620480, 93525427956, 87185947919, 47537280], 'label': '6912.ia.192.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '192.dn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565918
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.w1', '36.x1', '36.z1', '36.bb1', '36.bd1', '36.bf1', '36.bh1', '36.ey1', '36.ez1', '36.fc1', '36.fd1', '36.ft1', '36.fu1', '36.fy1', '36.fz1', '54.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.18.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565919
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.by1', '96.eg1', '96.dn1', '96.ev1', '96.ds1', '96.gl1'], 'contains': ['384.r1', '384.t1', '384.bj1', '576.ft1', '576.fx1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87218607813, 93405312000, 746, 2676], 'label': '6912.ia.192.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.do1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565920
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bz1', '96.eg1', '96.dn1', '96.ex1', '96.dt1', '96.gm1'], 'contains': ['384.r1', '384.ba1', '384.be1', '576.fu1', '576.fy1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87218607813, 93405312000, 40280426, 2676], 'label': '6912.ia.192.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '192.dp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565921
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ca1', '96.eh1', '96.do1', '96.ev1', '96.ex1', '96.ds1', '96.dt1'], 'contains': ['384.r1', '384.ba1', '384.bj1', '576.fv1', '576.fz1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [87218607813, 6851, 93405312000, 87096887], 'label': '6912.ia.192.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '192.dq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565922
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.cb1', '96.ei1', '96.dp1', '96.gl1', '96.gm1'], 'contains': ['384.r1', '384.bf1', '384.bk1', '576.fw1', '576.ga1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6851, 93405312000, 87265419333, 83468087], 'label': '6912.ia.192.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565923
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gp1', '64.n1', '96.cc1', '96.ep1'], 'contains': ['384.s1', '384.z1', '384.bl1', '576.gb1', '576.gc1', '576.gd1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 47537280, 87185948613, 87185912426], 'label': '6912.ia.192.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.ds1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ds1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565924
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.n1', '96.ch1', '96.en1', '96.fa1', '96.du1', '96.gl1'], 'contains': ['384.t1', '384.w1', '384.bk1', '576.gb1', '576.ge1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [87185947919, 87185911680, 93405312000, 2676], 'label': '6912.ia.192.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565925
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gr1', '64.n1', '96.ci1', '96.ee1'], 'contains': ['384.u1', '384.x1', '384.bn1', '576.gc1', '576.ge1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [120115956, 87185947919, 87185911680, 47537280], 'label': '6912.ia.192.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.du1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.du1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565926
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gs1', '64.n1', '96.cj1'], 'contains': ['384.v1', '384.y1', '384.bo1', '576.gd1', '576.ge1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [174404119680, 93525427956, 87185947919, 87185948613], 'label': '6912.ia.192.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '192.dv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565927
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ck1', '96.eo1', '96.fa1', '96.du1', '96.gm1'], 'contains': ['384.w1', '384.ba1', '384.bk1', '576.gf1', '576.gi1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6851, 87185911680, 93405312000, 87261768087], 'label': '6912.ia.192.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565928
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.gt1', '64.o1', '96.cl1', '96.ee1'], 'contains': ['384.x1', '384.bc1', '384.bi1', '576.gg1', '576.gj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [7656719, 120115956, 87185911680, 47537280], 'label': '6912.ia.192.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '192.dx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565929
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '9.c1'], 'contains': ['36.w1', '36.y1', '36.ba1', '36.bc1', '36.be1', '36.bg1', '36.bl1', '36.ex1', '36.fa1', '36.fb1', '36.fe1', '36.fs1', '36.fv1', '36.fx1', '36.ga1', '54.h1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.18.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565930
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.o1', '96.cm1', '96.en1', '96.fe1', '96.dv1', '96.gm1'], 'contains': ['384.w1', '384.be1', '384.bf1', '576.gg1', '576.gk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7656719, 87185911680, 93405312000, 2676], 'label': '6912.ia.192.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565931
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.cn1', '96.eo1', '96.fe1', '96.dv1', '96.gl1'], 'contains': ['384.w1', '384.bf1', '384.bj1', '576.gh1', '576.gl1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6851, 87185911680, 93405312000, 83476887], 'label': '6912.ia.192.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '192.dz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.dz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565932
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '192.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.gv1', '64.o1', '96.co1', '96.ep1'], 'contains': ['384.z1', '384.bb1', '384.bg1', '576.gj1', '576.gk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 47537280, 87185948613, 7621226], 'label': '6912.ia.192.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '192.ea1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ea1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243565933
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': ['32.k1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.lp1', '72.lt1', '72.lu1', '72.lv1', '108.fc1', '108.fj1', '108.fp1', '108.fu1', '108.fy1', '108.gc1', '108.gg1'], 'contains': ['432.dr1', '432.ds1', '432.eo1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 87109068, 40279680], 'label': '6912.ia.216.a1', 'mobius_quo': 0, 'mobius_sub': 216, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '72.b1', '72.c1'], 'normal_contains': ['864.a1', '864.b1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '3456.jo', 'quotient_action_image': '36.10', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243565934
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.i1', '108.a1', '108.b1', '108.eu1'], 'contains': ['432.a1', '432.b1', '432.d1', '432.es1', '432.et1', '432.l1', '432.n1', '432.bc1', '432.bo1', '432.fn1', '432.fo1', '432.ki1', '432.jz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565935
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1', '72.j1', '108.a1', '108.c1', '108.eu1'], 'contains': ['432.a1', '432.c1', '432.j1', '432.m1', '432.o1', '432.bn1', '432.bp1', '432.kj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 43909226, 87178291200, 36933, 87091200], 'label': '6912.ia.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565936
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '108.b1', '108.c1', '108.d1', '108.e1', '108.f1', '108.g1', '108.ev1'], 'contains': ['432.a1', '432.e1', '432.h1', '432.eu1', '432.ev1', '432.p1', '432.r1', '432.bq1', '432.bs1', '432.fp1', '432.fq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 36933, 87124129], 'label': '6912.ia.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565937
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '108.a1', '108.f1', '108.ev1'], 'contains': ['432.a1', '432.g1', '432.i1', '432.q1', '432.s1', '432.br1', '432.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 87178291200, 40297548, 36933], 'label': '6912.ia.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565938
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '108.b1', '108.h1', '108.ew1'], 'contains': ['432.b1', '432.d1', '432.h1', '432.ex1', '432.ez1', '432.be1', '432.bg1', '432.cd1', '432.ce1', '432.gm1', '432.go1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565939
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.n1', '108.h1', '108.i1', '108.eu1'], 'contains': ['432.b1', '432.f1', '432.j1', '432.bh1', '432.bi1', '432.cf1', '432.cg1', '432.kk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 43908480, 87178291200, 36933, 87091200], 'label': '6912.ia.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565940
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '9.c1'], 'contains': ['36.j1', '36.k1', '36.l1', '36.q1', '36.r1', '36.w1', '36.gp1', '36.gq1', '36.gr1', '36.gs1', '36.gt1', '36.bo1', '36.bp1', '36.bq1', '36.cw1', '36.cx1', '36.dc1', '36.gx1', '36.gy1', '36.gz1', '36.hn1', '36.ho1', '36.id1', '54.q1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 40279680, 127370880, 93405312000, 127380345, 7620480], 'label': '6912.ia.18.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bj1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565941
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '108.a1', '108.i1', '108.ew1'], 'contains': ['432.b1', '432.i1', '432.j1', '432.bj1', '432.bk1', '432.ch1', '432.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 43909226, 87178291200, 36933, 87091200], 'label': '6912.ia.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565942
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '108.a1', '108.h1', '108.ex1'], 'contains': ['432.b1', '432.c1', '432.g1', '432.ew1', '432.fb1', '432.bf1', '432.bl1', '432.bu1', '432.cj1', '432.gl1', '432.gp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 40280426, 87178291200, 36933, 87100665], 'label': '6912.ia.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565943
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '108.b1', '108.i1', '108.k1', '108.j1', '108.l1', '108.m1', '108.ex1'], 'contains': ['432.b1', '432.e1', '432.ew1', '432.ey1', '432.fa1', '432.bd1', '432.bm1', '432.ck1', '432.gk1', '432.gn1', '432.gq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565944
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.r1', '108.h1', '108.n1', '108.eu1'], 'contains': ['432.c1', '432.d1', '432.f1', '432.bv1', '432.by1', '432.cl1', '432.cr1', '432.kl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43908480, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565945
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '108.a1', '108.n1', '108.ew1'], 'contains': ['432.c1', '432.d1', '432.i1', '432.bw1', '432.bz1', '432.cm1', '432.cs1', '432.ka1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565946
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1', '108.c1', '108.h1', '108.ew1'], 'contains': ['432.c1', '432.h1', '432.j1', '432.ca1', '432.cb1', '432.ct1', '432.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 87178291200, 36933, 83471865, 87091200], 'label': '6912.ia.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565947
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '108.c1', '108.n1', '108.p1', '108.o1', '108.q1', '108.r1', '108.ex1'], 'contains': ['432.c1', '432.e1', '432.fa1', '432.fb1', '432.bx1', '432.cc1', '432.cv1', '432.gr1', '432.gs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 87127439, 40279680], 'label': '6912.ia.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565948
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1', '108.a1', '108.h1', '108.ey1'], 'contains': ['432.d1', '432.g1', '432.j1', '432.co1', '432.cp1', '432.cw1', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 43909226, 87178291200, 36933, 87091200], 'label': '6912.ia.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565949
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '108.b1', '108.n1', '108.t1', '108.s1', '108.u1', '108.v1', '108.ey1'], 'contains': ['432.d1', '432.e1', '432.fc1', '432.fd1', '432.cn1', '432.cq1', '432.cy1', '432.gt1', '432.gu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87178291200, 36933, 87100665], 'label': '6912.ia.216.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565950
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '108.i1', '108.n1', '108.w1', '108.x1', '108.y1', '108.bc1', '108.ev1'], 'contains': ['432.e1', '432.f1', '432.i1', '432.cz1', '432.db1', '432.du1', '432.ea1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87178291200, 36933, 119750400, 87124129], 'label': '6912.ia.216.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565951
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '9.c1'], 'contains': ['36.m1', '36.n1', '36.bf1', '36.bg1', '36.gq1', '36.gv1', '36.gw1', '36.br1', '36.bs1', '36.dd1', '36.de1', '36.hb1', '36.hc1', '36.if1', '36.ig1', '54.r1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 87178291200, 36933, 119769548, 40279680], 'label': '6912.ia.18.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243565952
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '108.f1', '108.k1', '108.p1', '108.t1', '108.ba1', '108.bc1', '108.ez1'], 'contains': ['432.e1', '432.i1', '432.dd1', '432.dh1', '432.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 43926348, 87178291200, 36933, 87124129], 'label': '6912.ia.216.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565953
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '108.g1', '108.j1', '108.o1', '108.s1', '108.y1', '108.z1', '108.ez1'], 'contains': ['432.e1', '432.h1', '432.ff1', '432.fk1', '432.dc1', '432.dg1', '432.eb1', '432.gx1', '432.hd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87178291200, 36933, 87124129, 83480268], 'label': '6912.ia.216.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565954
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '108.c1', '108.i1', '108.ba1', '108.z1', '108.bb1', '108.bd1', '108.ey1'], 'contains': ['432.e1', '432.j1', '432.df1', '432.di1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 87178291200, 36933, 87100665], 'label': '6912.ia.216.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565955
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '108.d1', '108.m1', '108.q1', '108.s1', '108.w1', '108.ba1', '108.fa1'], 'contains': ['432.e1', '432.fg1', '432.fh1', '432.dj1', '432.dl1', '432.gy1', '432.gz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 19148, 36933, 40279680], 'label': '6912.ia.216.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243565956
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '108.e1', '108.l1', '108.r1', '108.t1', '108.x1', '108.z1', '108.fa1'], 'contains': ['432.e1', '432.fh1', '432.dk1', '432.do1', '432.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 127390028, 87178291200, 36933, 40279680], 'label': '6912.ia.216.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565957
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '108.d1', '108.j1', '108.p1', '108.v1', '108.x1', '108.bb1', '108.fb1'], 'contains': ['432.e1', '432.fi1', '432.dm1', '432.dp1', '432.hb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.216.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565958
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '108.e1', '108.k1', '108.o1', '108.u1', '108.w1', '108.bd1', '108.fb1'], 'contains': ['432.e1', '432.fl1', '432.dn1', '432.dq1', '432.he1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.216.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565959
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1', '108.f1', '108.l1', '108.q1', '108.u1', '108.y1', '108.bb1', '108.fc1'], 'contains': ['432.e1', '432.g1', '432.fe1', '432.fm1', '432.de1', '432.dr1', '432.dw1', '432.gw1', '432.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 127370880, 40312609, 87178291200, 36933], 'label': '6912.ia.216.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243565960
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.bg1', '108.g1', '108.m1', '108.r1', '108.v1', '108.bc1', '108.bd1', '108.fc1'], 'contains': ['432.e1', '432.fe1', '432.fj1', '432.da1', '432.ds1', '432.gv1', '432.hc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.216.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565961
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1', '108.h1', '108.y1', '108.ev1'], 'contains': ['432.f1', '432.g1', '432.h1', '432.dt1', '432.dv1', '432.dx1', '432.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87178291200, 40297548, 36933, 119750400], 'label': '6912.ia.216.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565962
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.o1', '9.c1'], 'contains': ['36.a1', '36.o1', '36.p1', '36.bh1', '36.bl1', '36.gq1', '36.gu1', '36.bt1', '36.bu1', '36.df1', '36.dg1', '36.ha1', '36.hd1', '36.ie1', '36.ih1', '54.s1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.18.bl1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bl1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243565963
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '108.f1', '108.y1', '108.ez1'], 'contains': ['432.g1', '432.i1', '432.h1', '432.dy1', '432.dz1', '432.eg1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43941409, 127388748, 87178291200, 40297548, 36933], 'label': '6912.ia.216.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565964
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ir1', '72.is1', '72.ja1', '108.eu1', '108.ev1'], 'contains': ['432.a1', '432.f1', '432.eh1', '432.k1', '432.u1', '432.ei1', '432.ek1', '432.kb1', '432.km1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 87178291200, 36933, 40279680], 'label': '6912.ia.216.hn1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565965
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.it1', '72.iu1', '72.jb1', '108.eu1', '108.ew1', '108.ex1'], 'contains': ['432.b1', '432.c1', '432.eh1', '432.t1', '432.v1', '432.ej1', '432.el1', '432.kc1', '432.kn1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.216.ho1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '216.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ho1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565966
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iv1', '72.iw1', '72.ix1', '72.jc1', '108.eu1', '108.ew1', '108.ey1'], 'contains': ['432.d1', '432.j1', '432.eh1', '432.w1', '432.x1', '432.em1', '432.en1', '432.kd1', '432.ko1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.216.hp1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565967
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iy1', '72.jd1', '108.ev1', '108.ex1', '108.ey1', '108.ez1', '108.fa1', '108.fb1', '108.fc1'], 'contains': ['432.e1', '432.g1', '432.eh1', '432.y1', '432.z1', '432.eo1', '432.ep1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 36933, 40279680], 'label': '6912.ia.216.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243565968
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iz1', '72.je1', '108.ev1', '108.ew1', '108.ez1'], 'contains': ['432.i1', '432.h1', '432.eh1', '432.bb1', '432.ba1', '432.eq1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 127370880, 87178291200, 36933, 40279680], 'label': '6912.ia.216.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565969
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mj1', '108.b1'], 'contains': ['432.es1', '432.et1', '432.ev1', '432.ew1', '432.ex1', '432.ez1', '432.fd1', '432.fr1', '432.ft1', '432.fv1', '432.fy1', '432.hg1', '432.hi1', '432.hq1', '432.ht1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 7656719, 87178291200, 36933, 87100665], 'label': '6912.ia.216.is1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '216.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.is1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243565970
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lx1', '72.mk1', '108.b1', '108.gh1', '108.gi1'], 'contains': ['432.es1', '432.eu1', '432.ex1', '432.ey1', '432.fc1', '432.fs1', '432.fu1', '432.fz1', '432.hh1', '432.hj1', '432.hu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 7621226, 36933], 'label': '6912.ia.216.it1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.it1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565971
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ml1', '108.b1', '108.gj1', '108.gk1'], 'contains': ['432.et1', '432.eu1', '432.ez1', '432.fa1', '432.fc1', '432.fw1', '432.fx1', '432.ga1', '432.hr1', '432.hs1', '432.hv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 36933, 83498639], 'label': '6912.ia.216.iu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565972
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mm1', '108.g1', '108.gh1', '108.gj1'], 'contains': ['432.eu1', '432.ev1', '432.fe1', '432.ff1', '432.fk1', '432.gb1', '432.gd1', '432.gj1', '432.hw1', '432.hy1', '432.ie1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 87100665, 87124129], 'label': '6912.ia.216.iv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565973
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '9.c1'], 'contains': ['36.t1', '36.s1', '36.y1', '36.x1', '36.gs1', '36.gu1', '36.gw1', '36.cz1', '36.cy1', '36.di1', '36.dh1', '36.hs1', '36.ht1', '36.it1', '36.iu1', '54.t1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87178291200, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.18.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bm1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565974
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ly1', '72.mn1', '108.d1', '108.gi1', '108.gj1'], 'contains': ['432.eu1', '432.fg1', '432.fi1', '432.ge1', '432.gg1', '432.hz1', '432.ib1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 7654690, 36933], 'label': '6912.ia.216.iw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243565975
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mo1', '108.d1', '108.gh1', '108.gk1'], 'contains': ['432.eu1', '432.fh1', '432.fi1', '432.gf1', '432.gh1', '432.ia1', '432.ic1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 36933, 83496610], 'label': '6912.ia.216.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ix1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566288
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ix1', '72.mh1', '72.mi1', '96.bb1', '96.bj1'], 'contains': ['576.i1', '576.bg1', '576.bp1', '576.do1', '864.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87178291200, 43561327, 36933, 83468087], 'label': '6912.ia.288.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ci1', 'old_label': '288.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243565976
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lw1', '72.lz1', '72.mp1', '108.g1', '108.gi1', '108.gk1'], 'contains': ['432.eu1', '432.ff1', '432.fj1', '432.gc1', '432.gi1', '432.hx1', '432.id1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 36933], 'label': '6912.ia.216.iy1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243565977
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mq1', '108.l1', '108.m1', '108.gh1'], 'contains': ['432.ey1', '432.fe1', '432.fh1', '432.hk1', '432.hn1', '432.ip1', '432.is1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 87178291200, 36933, 746], 'label': '6912.ia.216.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565978
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ma1', '72.mr1', '108.j1', '108.gh1', '108.gi1'], 'contains': ['432.ey1', '432.ff1', '432.fi1', '432.hm1', '432.ho1', '432.ir1', '432.it1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 83495329, 83496610], 'label': '6912.ia.216.ja1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ja1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565979
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mb1', '72.mc1', '72.ms1', '108.m1', '108.gi1'], 'contains': ['432.ey1', '432.fg1', '432.fj1', '432.hl1', '432.hp1', '432.iq1', '432.iu1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 36933, 746], 'label': '6912.ia.216.jb1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565980
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mt1', '108.m1', '108.q1', '108.gj1'], 'contains': ['432.fa1', '432.fe1', '432.fg1', '432.if1', '432.ij1', '432.jf1', '432.jj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 87178291200, 36933, 127371626], 'label': '6912.ia.216.jc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565981
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mu1', '108.l1', '108.q1', '108.r1'], 'contains': ['432.fa1', '432.fe1', '432.fh1', '432.ig1', '432.ik1', '432.jg1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 40280426, 87178291200, 36933], 'label': '6912.ia.216.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565982
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mv1', '108.j1', '108.gj1', '108.gk1'], 'contains': ['432.fa1', '432.ff1', '432.fi1', '432.ii1', '432.il1', '432.ji1', '432.jl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 7654690, 36933, 83495329], 'label': '6912.ia.216.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.je1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565983
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.md1', '72.mw1', '108.m1', '108.r1', '108.gk1'], 'contains': ['432.fa1', '432.fh1', '432.fj1', '432.ih1', '432.im1', '432.jh1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 32929, 40280426, 87178291200, 36933], 'label': '6912.ia.216.jf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jf1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565984
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.s1', '9.c1'], 'contains': ['36.a1', '36.u1', '36.v1', '36.z1', '36.ba1', '36.gs1', '36.gv1', '36.da1', '36.db1', '36.dj1', '36.dk1', '36.hr1', '36.hu1', '36.is1', '36.iv1', '54.u1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.18.bn1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bn1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243565985
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mx1', '108.o1'], 'contains': ['432.fb1', '432.fk1', '432.fl1', '432.in1', '432.io1', '432.jn1', '432.jo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7653409, 87178291200, 43942690, 36933, 87100665], 'label': '6912.ia.216.jg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1', 'old_label': '216.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jg1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565986
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.my1', '108.v1', '108.gh1', '108.gj1'], 'contains': ['432.fc1', '432.fe1', '432.fi1', '432.iv1', '432.iz1', '432.jp1', '432.jt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.216.jh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565987
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mf1', '72.mz1', '108.s1', '108.gi1', '108.gj1'], 'contains': ['432.fc1', '432.ff1', '432.fg1', '432.ix1', '432.ja1', '432.jr1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 83498639, 83495329], 'label': '6912.ia.216.ji1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ji1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565988
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.na1', '108.s1', '108.gh1', '108.gk1'], 'contains': ['432.fc1', '432.ff1', '432.fh1', '432.iy1', '432.jb1', '432.js1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 7621226, 36933, 83495329], 'label': '6912.ia.216.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565989
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.me1', '72.mg1', '72.mh1', '72.nb1', '108.v1', '108.gi1', '108.gk1'], 'contains': ['432.fc1', '432.fi1', '432.fj1', '432.iw1', '432.jc1', '432.jq1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 7621226, 36933], 'label': '6912.ia.216.jk1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565990
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mi1', '72.nc1', '108.u1'], 'contains': ['432.fd1', '432.fl1', '432.fm1', '432.jd1', '432.je1', '432.jx1', '432.jy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87178291200, 40297548, 36933, 87100665, 83463146], 'label': '6912.ia.216.jl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.u1', 'old_label': '216.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jl1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243565991
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bj1', '72.bl1', '108.eu1', '108.be1', '108.bf1'], 'contains': ['432.k1', '432.l1', '432.o1', '432.t1', '432.w1', '432.bi1', '432.cl1', '432.kp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87218570880, 36933, 87091200, 83468087], 'label': '6912.ia.216.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565992
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bk1', '72.bm1', '108.eu1', '108.be1', '108.bg1'], 'contains': ['432.k1', '432.m1', '432.n1', '432.v1', '432.x1', '432.by1', '432.cg1', '432.kq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 36933, 87091200], 'label': '6912.ia.216.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565993
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1', '108.ev1', '108.bf1', '108.bg1', '108.bj1', '108.bh1', '108.bi1', '108.bk1'], 'contains': ['432.k1', '432.p1', '432.s1', '432.y1', '432.ba1', '432.db1', '432.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 87305662080, 32929, 36933, 87124129], 'label': '6912.ia.216.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565994
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1', '108.ev1', '108.be1', '108.bj1'], 'contains': ['432.k1', '432.r1', '432.q1', '432.z1', '432.bb1', '432.ea1', '432.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 87305662080, 40297548, 36933], 'label': '6912.ia.216.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565995
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '9.c1'], 'contains': ['36.bc1', '36.bb1', '36.bj1', '36.bi1', '36.gt1', '36.gu1', '36.gv1', '36.dm1', '36.dl1', '36.dq1', '36.dp1', '36.iz1', '36.ja1', '36.jj1', '36.jk1', '54.v1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 87178291200, 36933, 83480268, 40279680], 'label': '6912.ia.18.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bo1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243565996
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1', '108.b1', '108.be1', '108.fd1'], 'contains': ['432.l1', '432.n1', '432.r1', '432.bd1', '432.bg1', '432.cd1', '432.cn1', '432.fs1', '432.ft1', '432.fv1', '432.fw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.216.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243565997
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '108.a1', '108.bf1', '108.fd1'], 'contains': ['432.l1', '432.o1', '432.s1', '432.bf1', '432.bk1', '432.cm1', '432.cp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.216.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565998
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1', '108.a1', '108.be1', '108.fe1'], 'contains': ['432.l1', '432.m1', '432.q1', '432.bj1', '432.bl1', '432.bw1', '432.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127380345, 43909226, 36933, 87091200], 'label': '6912.ia.216.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '216.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243565999
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bs1', '108.b1', '108.bf1', '108.bl1', '108.bm1', '108.bn1', '108.bo1', '108.fe1'], 'contains': ['432.l1', '432.p1', '432.be1', '432.bm1', '432.cq1', '432.fr1', '432.fu1', '432.fx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 36933, 87100665], 'label': '6912.ia.216.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566000
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1', '108.a1', '108.bg1', '108.fd1'], 'contains': ['432.m1', '432.n1', '432.s1', '432.bu1', '432.bz1', '432.ci1', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 43909226, 36933, 87091200, 87305671545], 'label': '6912.ia.216.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566001
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1', '108.c1', '108.be1', '108.fd1'], 'contains': ['432.m1', '432.o1', '432.r1', '432.bx1', '432.cb1', '432.cu1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 43909226, 87265391865, 36933, 87091200], 'label': '6912.ia.216.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566002
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1', '108.c1', '108.bg1', '108.bp1', '108.bq1', '108.br1', '108.bs1', '108.fe1'], 'contains': ['432.m1', '432.p1', '432.ca1', '432.cc1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 36933, 87100665], 'label': '6912.ia.216.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566003
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bw1', '108.a1', '108.be1', '108.ff1'], 'contains': ['432.n1', '432.o1', '432.q1', '432.ch1', '432.cj1', '432.cs1', '432.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127380345, 87222200426, 36933, 87091200], 'label': '6912.ia.216.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566004
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1', '108.b1', '108.bg1', '108.bt1', '108.bu1', '108.bv1', '108.bw1', '108.ff1'], 'contains': ['432.n1', '432.p1', '432.ce1', '432.ck1', '432.cy1', '432.fy1', '432.fz1', '432.ga1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87185947919, 36933, 87100665], 'label': '6912.ia.216.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566005
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1', '108.c1', '108.bf1', '108.bx1', '108.by1', '108.bz1', '108.ca1', '108.ff1'], 'contains': ['432.o1', '432.p1', '432.ct1', '432.cv1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 87222200426, 36933, 87100665], 'label': '6912.ia.216.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566006
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['1152.bc1', '1152.be1', '1152.b1', '1152.w1', '1152.bs1', '1152.bw1', '1152.bv1', '1152.by1', '1152.bi1', '1152.bp1', '1152.bk1', '1152.br1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.d1', '12.f1', '12.i1', '18.bs1', '18.by1', '24.bp1', '24.dw1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': ['2.d1'], 'normal_contains': ['12.d1', '12.f1', '12.i1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243566007
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1', '6.v1', '6.w1', '9.c1'], 'contains': ['36.a1', '36.bd1', '36.be1', '36.bk1', '36.bm1', '36.gt1', '36.gw1', '36.dn1', '36.do1', '36.dr1', '36.ds1', '36.iy1', '36.jb1', '36.ji1', '36.jl1', '54.w1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.18.bp1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bp1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566008
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1', '108.g1', '108.bj1', '108.bl1', '108.bp1', '108.bt1', '108.bx1', '108.fg1'], 'contains': ['432.p1', '432.r1', '432.da1', '432.dg1', '432.eb1', '432.gc1', '432.gd1', '432.gj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87265400268, 87124129], 'label': '6912.ia.216.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566009
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1', '108.f1', '108.bk1', '108.bm1', '108.bq1', '108.bu1', '108.by1', '108.fg1'], 'contains': ['432.p1', '432.s1', '432.de1', '432.dh1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 87218588748, 36933, 87124129], 'label': '6912.ia.216.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566010
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1', '108.d1', '108.bh1', '108.bo1', '108.br1', '108.bt1', '108.by1', '108.fh1'], 'contains': ['432.p1', '432.dj1', '432.dm1', '432.ge1', '432.gf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 83481548], 'label': '6912.ia.216.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566011
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1', '108.e1', '108.bi1', '108.bn1', '108.bs1', '108.bu1', '108.bx1', '108.fh1'], 'contains': ['432.p1', '432.dk1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 119769548], 'label': '6912.ia.216.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566665
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fn1', '128.c1', '192.i1', '192.bz1', '192.dk1', '192.dm1'], 'contains': ['768.d1', '1152.s1', '1152.u1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [7620480, 120115956, 47537280], 'label': '6912.ia.384.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '384.p1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566012
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd1', '108.d1', '108.bi1', '108.bl1', '108.bq1', '108.bw1', '108.bz1', '108.fi1'], 'contains': ['432.p1', '432.dl1', '432.dp1', '432.gg1', '432.gh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 87261772748], 'label': '6912.ia.216.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566013
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ce1', '108.e1', '108.bh1', '108.bm1', '108.bp1', '108.bv1', '108.ca1', '108.fi1'], 'contains': ['432.p1', '432.do1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87100665, 87298060748], 'label': '6912.ia.216.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566014
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1', '108.f1', '108.bj1', '108.bn1', '108.br1', '108.bv1', '108.bz1', '108.fj1'], 'contains': ['432.p1', '432.q1', '432.dd1', '432.dr1', '432.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 40297548, 36933], 'label': '6912.ia.216.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566015
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1', '72.ci1', '72.cj1', '108.g1', '108.bk1', '108.bo1', '108.bs1', '108.bw1', '108.ca1', '108.fj1'], 'contains': ['432.p1', '432.dc1', '432.ds1', '432.gb1', '432.gi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.216.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566016
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1', '108.f1', '108.bj1', '108.fg1'], 'contains': ['432.r1', '432.q1', '432.s1', '432.dw1', '432.ec1', '432.dz1', '432.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127388748, 87218603809, 40297548, 36933], 'label': '6912.ia.216.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566017
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '72.cn1', '108.eu1', '108.cb1', '108.cc1'], 'contains': ['432.t1', '432.u1', '432.x1', '432.bc1', '432.bh1', '432.bp1', '432.cr1', '432.kr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 43909226, 43908480, 36933, 87091200], 'label': '6912.ia.216.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566018
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.bn1', '36.bz1', '36.cp1', '36.cr1', '36.cu1', '36.eh1', '36.fw1', '54.j1', '72.bj1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218570880, 32929, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566019
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.co1', '108.ew1', '108.bf1', '108.cb1'], 'contains': ['432.t1', '432.w1', '432.ba1', '432.be1', '432.bk1', '432.cm1', '432.ct1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.216.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566020
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1', '108.ew1', '108.be1', '108.cc1'], 'contains': ['432.t1', '432.x1', '432.bb1', '432.bg1', '432.bj1', '432.cs1', '432.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 87218570880, 43909226, 36933, 87091200], 'label': '6912.ia.216.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566021
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cq1', '108.ex1', '108.be1', '108.cb1'], 'contains': ['432.t1', '432.v1', '432.z1', '432.bd1', '432.bl1', '432.bx1', '432.cj1', '432.gk1', '432.gl1', '432.gp1', '432.gs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87218607813, 40280426, 36933, 87100665], 'label': '6912.ia.216.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566022
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cr1', '108.ex1', '108.bf1', '108.cc1', '108.cf1', '108.ce1', '108.cd1', '108.cg1'], 'contains': ['432.t1', '432.y1', '432.bf1', '432.bm1', '432.cv1', '432.gl1', '432.gn1', '432.gr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 36933, 87305699013, 40279680], 'label': '6912.ia.216.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566023
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1', '72.cs1', '108.eu1', '108.cb1', '108.ch1'], 'contains': ['432.u1', '432.v1', '432.w1', '432.bn1', '432.bo1', '432.bv1', '432.cf1', '432.ks1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 43908480, 36933, 87091200, 83468087], 'label': '6912.ia.216.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566024
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '108.ev1', '108.cc1', '108.ch1', '108.ck1', '108.ci1', '108.cj1', '108.cl1'], 'contains': ['432.u1', '432.y1', '432.bb1', '432.bq1', '432.bt1', '432.cz1', '432.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305662080, 32929, 36933, 119750400, 87124129], 'label': '6912.ia.216.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566025
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cu1', '108.ev1', '108.cb1', '108.ck1'], 'contains': ['432.u1', '432.z1', '432.ba1', '432.bs1', '432.br1', '432.du1', '432.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87305662080, 40297548, 36933, 119750400], 'label': '6912.ia.216.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566026
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cv1', '108.ew1', '108.be1', '108.ch1'], 'contains': ['432.v1', '432.w1', '432.bb1', '432.bw1', '432.cb1', '432.cd1', '432.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 87218570880, 36933, 87091200, 83468087], 'label': '6912.ia.216.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ch1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566027
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cw1', '108.ew1', '108.bg1', '108.cb1'], 'contains': ['432.v1', '432.x1', '432.ba1', '432.bz1', '432.ca1', '432.ce1', '432.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 43909226, 36933, 83471865, 87091200], 'label': '6912.ia.216.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ci1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566028
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '108.ex1', '108.bg1', '108.ch1', '108.co1', '108.cn1', '108.cm1', '108.cp1'], 'contains': ['432.v1', '432.y1', '432.bu1', '432.cc1', '432.ck1', '432.gp1', '432.gq1', '432.gr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87127439, 87305699013, 40279680], 'label': '6912.ia.216.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566029
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '9.a1'], 'contains': ['36.bn1', '36.ce1', '36.cj1', '36.ct1', '36.cv1', '36.fg1', '36.fq1', '54.l1', '72.bk1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566030
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1', '108.ey1', '108.be1', '108.cb1'], 'contains': ['432.w1', '432.x1', '432.z1', '432.cn1', '432.co1', '432.cw1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 43909226, 87305662080, 36933, 87091200], 'label': '6912.ia.216.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ck1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566031
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cz1', '108.ey1', '108.bf1', '108.ch1', '108.cs1', '108.cr1', '108.cq1', '108.ct1'], 'contains': ['432.w1', '432.y1', '432.cp1', '432.cq1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 36933, 87100665], 'label': '6912.ia.216.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566032
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '108.ey1', '108.bg1', '108.cc1', '108.cw1', '108.cv1', '108.cu1', '108.cx1'], 'contains': ['432.x1', '432.y1', '432.cx1', '432.cy1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 36933, 87100665], 'label': '6912.ia.216.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566033
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dh1', '108.fc1', '108.bj1', '108.cf1', '108.ck1', '108.co1', '108.cs1', '108.cw1'], 'contains': ['432.y1', '432.z1', '432.da1', '432.dr1', '432.dw1', '432.gv1', '432.gw1', '432.hf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 127370880, 87218570880, 40312609, 36933], 'label': '6912.ia.216.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ct1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566034
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '108.ez1', '108.bj1', '108.ce1', '108.cl1', '108.cn1', '108.cr1', '108.cv1'], 'contains': ['432.y1', '432.bb1', '432.dd1', '432.dg1', '432.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305662080, 32929, 43926348, 36933, 87124129], 'label': '6912.ia.216.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566035
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1', '108.ez1', '108.bk1', '108.cd1', '108.ck1', '108.cm1', '108.cq1', '108.cu1'], 'contains': ['432.y1', '432.ba1', '432.dc1', '432.dh1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305662080, 32929, 36933, 87124129, 83480268], 'label': '6912.ia.216.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cn1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566036
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '108.fa1', '108.bh1', '108.cg1', '108.ci1', '108.co1', '108.cq1', '108.cv1'], 'contains': ['432.y1', '432.dj1', '432.do1', '432.gy1', '432.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 19148, 36933, 87305699013, 40279680], 'label': '6912.ia.216.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566037
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.de1', '108.fa1', '108.bi1', '108.cf1', '108.cj1', '108.cp1', '108.cr1', '108.cu1'], 'contains': ['432.y1', '432.dk1', '432.dl1', '432.gz1', '432.ha1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 127390028, 36933, 87305699013, 40279680], 'label': '6912.ia.216.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566038
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.df1', '108.fb1', '108.bh1', '108.cd1', '108.cj1', '108.cn1', '108.ct1', '108.cw1'], 'contains': ['432.y1', '432.dm1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 36933, 87100665, 83481548], 'label': '6912.ia.216.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566039
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dg1', '108.fb1', '108.bi1', '108.ce1', '108.ci1', '108.cm1', '108.cs1', '108.cx1'], 'contains': ['432.y1', '432.dn1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218607813, 36933, 87100665, 119769548], 'label': '6912.ia.216.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566040
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.bp1', '36.bt1', '36.bs1', '36.bv1', '36.bx1', '36.cl1', '36.cn1', '36.da1', '36.cz1', '36.dn1', '36.dm1', '36.ea1', '36.ec1', '36.fs1', '36.fu1', '54.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 36933, 87218570880, 93405312000, 40297548, 7620480, 127388748, 7621226], 'label': '6912.ia.18.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566041
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '72.di1', '108.fc1', '108.bk1', '108.cg1', '108.cl1', '108.cp1', '108.ct1', '108.cx1'], 'contains': ['432.y1', '432.de1', '432.ds1', '432.gw1', '432.hc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.216.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566042
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1', '108.ez1', '108.bj1', '108.ck1'], 'contains': ['432.z1', '432.bb1', '432.ba1', '432.ec1', '432.eb1', '432.dy1', '432.dz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43941409, 127388748, 87305662080, 40297548, 36933], 'label': '6912.ia.216.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cv1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566043
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dk1', '108.b1', '108.cb1', '108.fk1'], 'contains': ['432.bc1', '432.bd1', '432.be1', '432.bo1', '432.bs1', '432.ce1', '432.cn1', '432.hh1', '432.hi1', '432.hq1', '432.hr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87265391865, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.216.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566044
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1', '108.a1', '108.cc1', '108.fk1'], 'contains': ['432.bc1', '432.bf1', '432.bj1', '432.bp1', '432.bt1', '432.cs1', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 43909226, 36933, 87091200, 87305671545], 'label': '6912.ia.216.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cx1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566045
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dm1', '108.a1', '108.cb1', '108.fl1'], 'contains': ['432.bc1', '432.bk1', '432.bl1', '432.bn1', '432.br1', '432.bz1', '432.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 87185911680, 87222200426, 36933, 87091200], 'label': '6912.ia.216.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566046
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dn1', '108.i1', '108.cb1', '108.fd1'], 'contains': ['432.bd1', '432.bh1', '432.bk1', '432.cf1', '432.ci1', '432.du1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 43908480, 87265391865, 36933, 87091200], 'label': '6912.ia.216.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566047
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.do1', '108.i1', '108.be1', '108.fk1'], 'contains': ['432.bd1', '432.bi1', '432.bj1', '432.cg1', '432.ch1', '432.ea1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 43909226, 87265391865, 36933, 87091200], 'label': '6912.ia.216.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.da1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566048
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dp1', '108.h1', '108.bf1', '108.fk1'], 'contains': ['432.be1', '432.bf1', '432.bi1', '432.cl1', '432.cp1', '432.ct1', '432.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 83471865, 87091200, 83468087, 87305671545], 'label': '6912.ia.216.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.db1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566049
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dq1', '108.h1', '108.cc1', '108.fd1'], 'contains': ['432.bf1', '432.bg1', '432.bh1', '432.cr1', '432.cu1', '432.cx1', '432.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 43908480, 36933, 87091200, 87305671545], 'label': '6912.ia.216.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566050
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dr1', '108.h1', '108.cb1', '108.fe1'], 'contains': ['432.be1', '432.bh1', '432.bl1', '432.bv1', '432.ca1', '432.co1', '432.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 36933, 119750400, 87091200], 'label': '6912.ia.216.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '216.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566051
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.c1'], 'contains': ['36.bp1', '36.br1', '36.bu1', '36.bw1', '36.by1', '36.cm1', '36.co1', '36.cy1', '36.db1', '36.dl1', '36.do1', '36.eb1', '36.ee1', '36.ft1', '36.fv1', '54.j1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87218570880, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.18.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566052
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ds1', '108.h1', '108.be1', '108.fl1'], 'contains': ['432.bg1', '432.bi1', '432.bl1', '432.by1', '432.cb1', '432.cw1', '432.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 87222200426, 36933, 87091200, 87298041600], 'label': '6912.ia.216.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.de1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566053
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dt1', '108.b1', '108.cc1', '108.cy1', '108.cz1', '108.da1', '108.db1', '108.fl1'], 'contains': ['432.bc1', '432.bg1', '432.bm1', '432.bq1', '432.cy1', '432.hg1', '432.hj1', '432.hs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 87185911680, 36933, 87100665], 'label': '6912.ia.216.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.df1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566054
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1', '108.i1', '108.cc1', '108.dc1', '108.dd1', '108.de1', '108.di1', '108.fe1'], 'contains': ['432.bh1', '432.bj1', '432.bm1', '432.cz1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 43945413, 36933, 87100665], 'label': '6912.ia.216.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566055
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dv1', '108.m1', '108.bl1', '108.cf1', '108.cy1', '108.dc1', '108.df1', '108.fm1'], 'contains': ['432.bm1', '432.da1', '432.dl1', '432.hl1', '432.hn1', '432.ih1', '432.ij1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 87218588748, 36933, 40279680], 'label': '6912.ia.216.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566056
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dw1', '108.i1', '108.bf1', '108.df1', '108.dg1', '108.dh1', '108.dj1', '108.fl1'], 'contains': ['432.bi1', '432.bk1', '432.bm1', '432.db1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222200426, 87222236613, 36933, 87100665], 'label': '6912.ia.216.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.di1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566057
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dy1', '108.k1', '108.bn1', '108.ce1', '108.cz1', '108.df1', '108.di1', '108.fn1'], 'contains': ['432.bm1', '432.dd1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 119769548], 'label': '6912.ia.216.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dk1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566058
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dx1', '108.j1', '108.bo1', '108.cd1', '108.cy1', '108.de1', '108.dg1', '108.fn1'], 'contains': ['432.bm1', '432.dc1', '432.dm1', '432.hm1', '432.ii1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.216.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566059
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dz1', '108.l1', '108.bm1', '108.cg1', '108.cz1', '108.dd1', '108.dg1', '108.fm1'], 'contains': ['432.bm1', '432.de1', '432.do1', '432.hn1', '432.ik1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 36933, 87265400268, 40279680], 'label': '6912.ia.216.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dl1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566060
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ea1', '108.j1', '108.bl1', '108.ce1', '108.db1', '108.dd1', '108.dh1', '108.fo1'], 'contains': ['432.bm1', '432.dg1', '432.dp1', '432.ho1', '432.il1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87261771468, 87261772748], 'label': '6912.ia.216.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dm1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566061
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eb1', '108.k1', '108.bm1', '108.cd1', '108.da1', '108.dc1', '108.dj1', '108.fo1'], 'contains': ['432.bm1', '432.dh1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 36933, 87100665, 87298060748], 'label': '6912.ia.216.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dn1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566062
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.bq1', '36.bt1', '36.br1', '36.ca1', '36.cc1', '36.cf1', '36.ch1', '36.dj1', '36.di1', '36.dr1', '36.dq1', '36.fb1', '36.fd1', '36.fk1', '36.fm1', '54.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 36933, 43909226, 87218570880, 93405312000, 40297548, 7620480, 127388748], 'label': '6912.ia.18.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566063
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ec1', '108.l1', '108.bn1', '108.cf1', '108.da1', '108.de1', '108.dh1', '108.fp1'], 'contains': ['432.bm1', '432.dk1', '432.dr1', '432.hk1', '432.ig1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 36933, 746], 'label': '6912.ia.216.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.do1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566064
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ed1', '72.ee1', '108.m1', '108.bo1', '108.cg1', '108.db1', '108.di1', '108.dj1', '108.fp1'], 'contains': ['432.bm1', '432.dj1', '432.ds1', '432.hk1', '432.hp1', '432.if1', '432.im1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40280426, 40297548, 36933, 40279680], 'label': '6912.ia.216.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566065
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eg1', '108.a1', '108.ch1', '108.fk1'], 'contains': ['432.bn1', '432.bo1', '432.bt1', '432.bu1', '432.bw1', '432.ch1', '432.cp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.216.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dq1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566066
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eh1', '108.c1', '108.cb1', '108.fk1'], 'contains': ['432.bn1', '432.bp1', '432.bs1', '432.bx1', '432.ca1', '432.ct1', '432.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 87265391865, 36933, 83471865, 87091200], 'label': '6912.ia.216.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566067
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ei1', '108.c1', '108.ch1', '108.dk1', '108.dl1', '108.dm1', '108.dn1', '108.fl1'], 'contains': ['432.bn1', '432.bq1', '432.cb1', '432.cc1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 87222200426, 36933, 87100665], 'label': '6912.ia.216.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ds1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566068
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1', '108.a1', '108.cb1', '108.fq1'], 'contains': ['432.bo1', '432.bp1', '432.br1', '432.ci1', '432.cj1', '432.cm1', '432.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 87185911680, 43909226, 36933, 87091200], 'label': '6912.ia.216.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dt1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566069
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ek1', '108.b1', '108.ch1', '108.do1', '108.dp1', '108.dq1', '108.dr1', '108.fq1'], 'contains': ['432.bo1', '432.bq1', '432.cd1', '432.ck1', '432.cq1', '432.ht1', '432.hu1', '432.hv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87185911680, 36933, 87100665], 'label': '6912.ia.216.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.du1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566070
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1', '108.c1', '108.cc1', '108.ds1', '108.dt1', '108.du1', '108.dv1', '108.fq1'], 'contains': ['432.bp1', '432.bq1', '432.cu1', '432.cv1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 43909226, 36933, 87100665], 'label': '6912.ia.216.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566071
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.em1', '108.g1', '108.ck1', '108.cy1', '108.dk1', '108.do1', '108.ds1', '108.fr1'], 'contains': ['432.bq1', '432.bs1', '432.da1', '432.dc1', '432.eb1', '432.hx1', '432.hy1', '432.ie1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 87265400268, 87124129, 83480268], 'label': '6912.ia.216.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dw1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566072
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.en1', '108.f1', '108.cl1', '108.cz1', '108.dl1', '108.dp1', '108.dt1', '108.fr1'], 'contains': ['432.bq1', '432.bt1', '432.dd1', '432.de1', '432.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 43926348, 87218588748, 36933, 87124129], 'label': '6912.ia.216.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566073
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '9.c1'], 'contains': ['36.bq1', '36.bs1', '36.bu1', '36.cb1', '36.cd1', '36.cg1', '36.ci1', '36.dh1', '36.dk1', '36.dp1', '36.ds1', '36.fc1', '36.fe1', '36.fl1', '36.fo1', '54.l1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87218570880, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.18.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566074
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eo1', '108.d1', '108.ci1', '108.db1', '108.dm1', '108.do1', '108.dt1', '108.fs1'], 'contains': ['432.bq1', '432.dj1', '432.dp1', '432.hz1', '432.ia1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87100665, 87261772748], 'label': '6912.ia.216.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566075
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ep1', '108.e1', '108.cj1', '108.da1', '108.dn1', '108.dp1', '108.ds1', '108.fs1'], 'contains': ['432.bq1', '432.dk1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87100665, 87298060748], 'label': '6912.ia.216.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566076
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eq1', '108.d1', '108.cj1', '108.cy1', '108.dl1', '108.dr1', '108.du1', '108.ft1'], 'contains': ['432.bq1', '432.dl1', '432.dm1', '432.ib1', '432.ic1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87100665, 83481548], 'label': '6912.ia.216.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566077
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.er1', '108.e1', '108.ci1', '108.cz1', '108.dk1', '108.dq1', '108.dv1', '108.ft1'], 'contains': ['432.bq1', '432.dn1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87100665, 119769548], 'label': '6912.ia.216.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566078
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.es1', '108.f1', '108.ck1', '108.da1', '108.dm1', '108.dq1', '108.du1', '108.fu1'], 'contains': ['432.bq1', '432.br1', '432.dh1', '432.dr1', '432.dz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 40297548, 36933], 'label': '6912.ia.216.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ec1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566079
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ef1', '72.et1', '108.g1', '108.cl1', '108.db1', '108.dn1', '108.dr1', '108.dv1', '108.fu1'], 'contains': ['432.bq1', '432.dg1', '432.ds1', '432.hw1', '432.id1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.216.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566080
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eu1', '108.f1', '108.ck1', '108.fr1'], 'contains': ['432.bs1', '432.br1', '432.bt1', '432.dw1', '432.ec1', '432.dy1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43941409, 127388748, 87218603809, 40297548, 36933], 'label': '6912.ia.216.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ee1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566081
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ev1', '108.h1', '108.ch1', '108.fd1'], 'contains': ['432.bu1', '432.bv1', '432.cb1', '432.cd1', '432.cf1', '432.cp1', '432.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43908480, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.216.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ef1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566082
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ew1', '108.h1', '108.bg1', '108.fk1'], 'contains': ['432.bu1', '432.by1', '432.ca1', '432.ce1', '432.cg1', '432.cx1', '432.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 36933, 83471865, 87091200, 87305671545], 'label': '6912.ia.216.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eg1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566083
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ex1', '108.n1', '108.cb1', '108.fd1'], 'contains': ['432.bv1', '432.bx1', '432.bz1', '432.cm1', '432.cn1', '432.cr1', '432.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43908480, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.216.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eh1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566084
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.cr1', '36.cs1', '36.cv1', '36.ef1', '36.eg1', '36.ek1', '36.gb1', '54.n1', '72.ck1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 43909226, 32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566085
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ey1', '108.n1', '108.be1', '108.fk1'], 'contains': ['432.bw1', '432.bx1', '432.by1', '432.cl1', '432.cn1', '432.cs1', '432.ea1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.216.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ei1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566290
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iz1', '96.bl1', '144.hj1', '144.hk1', '144.ho1'], 'contains': ['576.h1', '576.bz1', '576.ca1', '864.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178291200, 79833600, 36933, 83495329], 'label': '6912.ia.288.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566086
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ez1', '108.n1', '108.ch1', '108.dw1', '108.dx1', '108.dy1', '108.dz1', '108.fe1'], 'contains': ['432.bv1', '432.bw1', '432.cc1', '432.cq1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 43945413, 36933, 87100665], 'label': '6912.ia.216.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ej1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566087
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fa1', '108.n1', '108.bg1', '108.ea1', '108.eb1', '108.ec1', '108.ed1', '108.fl1'], 'contains': ['432.by1', '432.bz1', '432.cc1', '432.cy1', '432.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 87222236613, 36933, 87100665], 'label': '6912.ia.216.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ek1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566088
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fb1', '108.r1', '108.bp1', '108.co1', '108.dk1', '108.dw1', '108.ea1', '108.fm1'], 'contains': ['432.cc1', '432.da1', '432.do1', '432.ih1', '432.ik1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218588748, 36933, 87127439, 40279680], 'label': '6912.ia.216.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.el1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566089
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fd1', '108.p1', '108.br1', '108.cn1', '108.dl1', '108.dz1', '108.ea1', '108.fn1'], 'contains': ['432.cc1', '432.dd1', '432.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 83481548], 'label': '6912.ia.216.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.en1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566090
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fc1', '108.o1', '108.bs1', '108.cm1', '108.dk1', '108.dy1', '108.eb1', '108.fn1'], 'contains': ['432.cc1', '432.dc1', '432.dn1', '432.in1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.216.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.em1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566091
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fe1', '108.q1', '108.bq1', '108.cp1', '108.dl1', '108.dx1', '108.eb1', '108.fm1'], 'contains': ['432.cc1', '432.de1', '432.dl1', '432.ij1', '432.ik1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87127439, 87265400268, 40279680], 'label': '6912.ia.216.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eo1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566092
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ff1', '108.o1', '108.bp1', '108.cn1', '108.dn1', '108.dx1', '108.ec1', '108.fo1'], 'contains': ['432.cc1', '432.dg1', '432.dq1', '432.io1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87298060748, 87261771468], 'label': '6912.ia.216.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ep1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566093
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1', '108.p1', '108.bq1', '108.cm1', '108.dm1', '108.dw1', '108.ed1', '108.fo1'], 'contains': ['432.cc1', '432.dh1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 36933, 87100665, 87261772748], 'label': '6912.ia.216.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566094
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fh1', '108.q1', '108.br1', '108.co1', '108.dm1', '108.dy1', '108.ec1', '108.fp1'], 'contains': ['432.cc1', '432.dj1', '432.dr1', '432.if1', '432.ig1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 40280426, 40297548, 36933], 'label': '6912.ia.216.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.er1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566095
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.a1'], 'contains': ['36.cs1', '36.ct1', '36.cu1', '36.ei1', '36.ej1', '36.ff1', '36.fp1', '54.p1', '72.cl1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 32929, 43908480, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.18.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566096
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fi1', '72.fj1', '108.r1', '108.bs1', '108.cp1', '108.dn1', '108.dz1', '108.ed1', '108.fp1'], 'contains': ['432.cc1', '432.dk1', '432.ds1', '432.ig1', '432.im1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 40297548, 36933, 40279680], 'label': '6912.ia.216.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.es1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566097
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fk1', '108.h1', '108.be1', '108.fq1'], 'contains': ['432.cd1', '432.cg1', '432.cj1', '432.cl1', '432.co1', '432.cu1', '432.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 43909226, 36933, 87091200, 87298041600], 'label': '6912.ia.216.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566098
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fl1', '108.h1', '108.cb1', '108.ff1'], 'contains': ['432.ce1', '432.cf1', '432.cj1', '432.cr1', '432.ct1', '432.cw1', '432.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 87222200426, 36933, 119750400, 87091200], 'label': '6912.ia.216.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566099
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fm1', '108.i1', '108.ch1', '108.ee1', '108.ef1', '108.eg1', '108.ek1', '108.ff1'], 'contains': ['432.cf1', '432.ch1', '432.ck1', '432.cz1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 87222200426, 36933, 87100665], 'label': '6912.ia.216.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ev1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566100
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fn1', '108.m1', '108.bt1', '108.co1', '108.do1', '108.ee1', '108.eh1', '108.fv1'], 'contains': ['432.ck1', '432.da1', '432.dj1', '432.iq1', '432.is1', '432.jh1', '432.jj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218588748, 19148, 36933, 40279680], 'label': '6912.ia.216.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ew1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566101
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fo1', '108.i1', '108.bg1', '108.eh1', '108.ei1', '108.ej1', '108.el1', '108.fq1'], 'contains': ['432.cg1', '432.ci1', '432.ck1', '432.db1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 87222236613, 36933, 87100665], 'label': '6912.ia.216.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ex1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566102
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fq1', '108.k1', '108.bv1', '108.cn1', '108.dp1', '108.eh1', '108.ek1', '108.fw1'], 'contains': ['432.ck1', '432.dd1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 87298060748], 'label': '6912.ia.216.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ez1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566103
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fp1', '108.j1', '108.bw1', '108.cm1', '108.do1', '108.eg1', '108.ei1', '108.fw1'], 'contains': ['432.ck1', '432.dc1', '432.dp1', '432.ir1', '432.ji1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87261772748, 83480268], 'label': '6912.ia.216.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ey1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566104
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fr1', '108.l1', '108.bu1', '108.cp1', '108.dp1', '108.ef1', '108.ei1', '108.fv1'], 'contains': ['432.ck1', '432.de1', '432.dk1', '432.is1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 127390028, 36933, 87265400268, 40279680], 'label': '6912.ia.216.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fa1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566105
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fs1', '108.j1', '108.bt1', '108.cn1', '108.dr1', '108.ef1', '108.ej1', '108.fx1'], 'contains': ['432.ck1', '432.dg1', '432.dm1', '432.it1', '432.jl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87261771468, 83481548], 'label': '6912.ia.216.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566106
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.cx1', '36.da1', '36.cy1', '36.df1', '36.de1', '36.dr1', '36.dp1', '36.dt1', '36.dv1', '36.dx1', '36.dz1', '36.et1', '36.ev1', '36.fx1', '36.fz1', '54.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43909226, 93405312000, 43908480, 40297548, 36933], 'label': '6912.ia.18.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566107
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ft1', '108.k1', '108.bu1', '108.cm1', '108.dq1', '108.ee1', '108.el1', '108.fx1'], 'contains': ['432.ck1', '432.dh1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 36933, 87100665, 119769548], 'label': '6912.ia.216.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566108
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fu1', '108.l1', '108.bv1', '108.co1', '108.dq1', '108.eg1', '108.ej1', '108.fy1'], 'contains': ['432.ck1', '432.do1', '432.dr1', '432.ip1', '432.jg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 36933, 87178291946], 'label': '6912.ia.216.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566109
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fv1', '72.fw1', '72.fx1', '108.m1', '108.bw1', '108.cp1', '108.dr1', '108.ek1', '108.el1', '108.fy1'], 'contains': ['432.ck1', '432.dl1', '432.ds1', '432.ip1', '432.iu1', '432.jf1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 40297548, 87218571626, 36933, 40279680], 'label': '6912.ia.216.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fe1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566110
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fy1', '108.n1', '108.bf1', '108.em1', '108.en1', '108.eo1', '108.ep1', '108.fq1'], 'contains': ['432.cl1', '432.cm1', '432.cq1', '432.cv1', '432.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 87222236613, 36933, 87100665], 'label': '6912.ia.216.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ff1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566111
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fz1', '108.v1', '108.bl1', '108.cs1', '108.do1', '108.dw1', '108.em1', '108.fz1'], 'contains': ['432.cq1', '432.da1', '432.dp1', '432.iw1', '432.iz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 87265400268], 'label': '6912.ia.216.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566112
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gb1', '108.t1', '108.bn1', '108.cr1', '108.dp1', '108.dz1', '108.em1', '108.ga1'], 'contains': ['432.cq1', '432.dd1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 36933, 87100665], 'label': '6912.ia.216.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fi1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566113
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ga1', '108.s1', '108.bo1', '108.cq1', '108.do1', '108.dy1', '108.en1', '108.ga1'], 'contains': ['432.cq1', '432.dc1', '432.dj1', '432.ix1', '432.iy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 83480268], 'label': '6912.ia.216.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fh1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566114
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gc1', '108.u1', '108.bm1', '108.ct1', '108.dp1', '108.dx1', '108.en1', '108.fz1'], 'contains': ['432.cq1', '432.de1', '432.dq1', '432.jd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 87305679948], 'label': '6912.ia.216.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fj1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566115
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gd1', '108.s1', '108.bl1', '108.cr1', '108.dr1', '108.dx1', '108.eo1', '108.gb1'], 'contains': ['432.cq1', '432.dg1', '432.dl1', '432.ja1', '432.jb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665, 87261771468], 'label': '6912.ia.216.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fk1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566116
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ge1', '108.t1', '108.bm1', '108.cq1', '108.dq1', '108.dw1', '108.ep1', '108.gb1'], 'contains': ['432.cq1', '432.dh1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 7656719, 9465, 36933, 87100665], 'label': '6912.ia.216.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566117
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.d1', '12.bm1', '12.cn1', '18.y1', '18.bb1', '24.bb1', '24.da1'], 'core': '12.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243566118
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.c1'], 'contains': ['36.cx1', '36.cz1', '36.db1', '36.dd1', '36.dg1', '36.dq1', '36.ds1', '36.du1', '36.dw1', '36.dy1', '36.ed1', '36.eu1', '36.ew1', '36.fy1', '36.ga1', '54.n1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 43908480, 87218570880, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.18.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566119
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gf1', '108.u1', '108.bn1', '108.cs1', '108.dq1', '108.dy1', '108.eo1', '108.gc1'], 'contains': ['432.cq1', '432.dn1', '432.dr1', '432.je1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 7621226, 36933], 'label': '6912.ia.216.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566120
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gg1', '72.gh1', '108.v1', '108.bo1', '108.ct1', '108.dr1', '108.dz1', '108.ep1', '108.gc1'], 'contains': ['432.cq1', '432.dm1', '432.ds1', '432.iv1', '432.jc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.216.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fn1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566121
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gi1', '108.n1', '108.cc1', '108.eq1', '108.er1', '108.es1', '108.et1', '108.ff1'], 'contains': ['432.cr1', '432.cs1', '432.cv1', '432.cy1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 43945413, 36933, 87100665], 'label': '6912.ia.216.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fo1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566122
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gj1', '108.r1', '108.bx1', '108.cf1', '108.ds1', '108.em1', '108.eq1', '108.fv1'], 'contains': ['432.cv1', '432.da1', '432.dk1', '432.jh1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 127390028, 87218588748, 36933, 40279680], 'label': '6912.ia.216.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fp1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566123
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gl1', '108.p1', '108.bz1', '108.ce1', '108.dt1', '108.em1', '108.et1', '108.fw1'], 'contains': ['432.cv1', '432.dd1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 36933, 87100665, 87261772748], 'label': '6912.ia.216.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fr1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566124
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gk1', '108.o1', '108.ca1', '108.cd1', '108.ds1', '108.en1', '108.es1', '108.fw1'], 'contains': ['432.cv1', '432.dc1', '432.dq1', '432.jn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87298060748, 83480268], 'label': '6912.ia.216.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fq1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566125
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gm1', '108.q1', '108.by1', '108.cg1', '108.dt1', '108.en1', '108.er1', '108.fv1'], 'contains': ['432.cv1', '432.de1', '432.dj1', '432.jj1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 19148, 36933, 87265400268, 40279680], 'label': '6912.ia.216.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fs1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566126
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gn1', '108.o1', '108.bx1', '108.ce1', '108.dv1', '108.eo1', '108.er1', '108.fx1'], 'contains': ['432.cv1', '432.dg1', '432.dn1', '432.jo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87261771468, 119769548], 'label': '6912.ia.216.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ft1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566127
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.go1', '108.p1', '108.by1', '108.cd1', '108.du1', '108.ep1', '108.eq1', '108.fx1'], 'contains': ['432.cv1', '432.dh1', '432.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 36933, 87100665, 83481548], 'label': '6912.ia.216.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fu1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566128
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gp1', '108.q1', '108.bz1', '108.cf1', '108.du1', '108.eo1', '108.es1', '108.fy1'], 'contains': ['432.cv1', '432.dl1', '432.dr1', '432.jf1', '432.jg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 87218571626, 36933], 'label': '6912.ia.216.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fv1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566129
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1'], 'contains': ['36.dc1', '36.df1', '36.dd1', '36.dj1', '36.dh1', '36.dn1', '36.dl1', '36.el1', '36.en1', '36.ep1', '36.er1', '36.ex1', '36.ez1', '36.fh1', '36.fj1', '54.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 93405312000, 43908480, 40297548, 7621226, 36933], 'label': '6912.ia.18.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566130
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gq1', '72.gr1', '72.gs1', '108.r1', '108.ca1', '108.cg1', '108.dv1', '108.ep1', '108.et1', '108.fy1'], 'contains': ['432.cv1', '432.do1', '432.ds1', '432.jg1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305681228, 40312609, 40297548, 36933, 40279680], 'label': '6912.ia.216.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fw1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566131
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gt1', '108.v1', '108.bt1', '108.cw1', '108.cy1', '108.ea1', '108.eq1', '108.gd1'], 'contains': ['432.cy1', '432.da1', '432.dm1', '432.jq1', '432.jt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.216.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fx1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566132
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gv1', '108.t1', '108.bv1', '108.cv1', '108.cz1', '108.ea1', '108.et1', '108.ge1'], 'contains': ['432.cy1', '432.dd1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87185947919, 36933, 87100665], 'label': '6912.ia.216.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566133
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gu1', '108.s1', '108.bw1', '108.cu1', '108.cy1', '108.eb1', '108.es1', '108.ge1'], 'contains': ['432.cy1', '432.dc1', '432.dl1', '432.jr1', '432.js1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 36933, 87100665, 83480268], 'label': '6912.ia.216.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fy1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566134
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gw1', '108.u1', '108.bu1', '108.cx1', '108.cz1', '108.eb1', '108.er1', '108.gd1'], 'contains': ['432.cy1', '432.de1', '432.dn1', '432.jx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.216.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ga1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566135
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gx1', '108.s1', '108.bt1', '108.cv1', '108.db1', '108.ec1', '108.er1', '108.gf1'], 'contains': ['432.cy1', '432.dg1', '432.dj1', '432.ju1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 36933, 87100665, 87261771468], 'label': '6912.ia.216.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566136
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gy1', '108.t1', '108.bu1', '108.cu1', '108.da1', '108.ed1', '108.eq1', '108.gf1'], 'contains': ['432.cy1', '432.dh1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 87185947919, 36933, 87100665], 'label': '6912.ia.216.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gc1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566137
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gz1', '108.u1', '108.bv1', '108.cw1', '108.da1', '108.ec1', '108.es1', '108.gg1'], 'contains': ['432.cy1', '432.dq1', '432.dr1', '432.jy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 36933, 87185912426], 'label': '6912.ia.216.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gd1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566138
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ha1', '72.hb1', '72.hc1', '108.v1', '108.bw1', '108.cx1', '108.db1', '108.ed1', '108.et1', '108.gg1'], 'contains': ['432.cy1', '432.dp1', '432.ds1', '432.jp1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.216.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ge1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566139
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hd1', '108.bc1', '108.ck1', '108.dc1', '108.dw1', '108.ee1', '108.eq1', '108.fg1'], 'contains': ['432.cz1', '432.da1', '432.dh1', '432.du1', '432.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 119750400, 87265400268, 87124129], 'label': '6912.ia.216.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gf1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566140
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.c1'], 'contains': ['36.dc1', '36.de1', '36.dg1', '36.di1', '36.dk1', '36.dm1', '36.do1', '36.em1', '36.eo1', '36.eq1', '36.es1', '36.ey1', '36.fa1', '36.fi1', '36.fn1', '54.p1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43908480, 87218570880, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.18.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566141
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.he1', '108.y1', '108.cl1', '108.dd1', '108.dx1', '108.ef1', '108.er1', '108.fg1'], 'contains': ['432.cz1', '432.de1', '432.dg1', '432.dv1', '432.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87218588748, 36933, 119750400, 87124129], 'label': '6912.ia.216.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566142
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hf1', '108.w1', '108.ci1', '108.di1', '108.dy1', '108.ee1', '108.er1', '108.fh1'], 'contains': ['432.cz1', '432.dj1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.216.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566143
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hg1', '108.x1', '108.cj1', '108.de1', '108.dz1', '108.ef1', '108.eq1', '108.fh1'], 'contains': ['432.cz1', '432.dk1', '432.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.216.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566144
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hh1', '108.w1', '108.cj1', '108.dc1', '108.dx1', '108.ek1', '108.es1', '108.fi1'], 'contains': ['432.cz1', '432.dl1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 87298060748], 'label': '6912.ia.216.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566145
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hi1', '108.x1', '108.ci1', '108.dd1', '108.dw1', '108.eg1', '108.et1', '108.fi1'], 'contains': ['432.cz1', '432.do1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43945413, 36933, 87100665, 87261772748], 'label': '6912.ia.216.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566146
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hj1', '108.y1', '108.ck1', '108.de1', '108.dy1', '108.eg1', '108.es1', '108.fj1'], 'contains': ['432.cz1', '432.dc1', '432.dr1', '432.dt1', '432.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 40297548, 36933], 'label': '6912.ia.216.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gl1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566147
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hk1', '108.bc1', '108.bj1', '108.df1', '108.ea1', '108.eh1', '108.em1', '108.fr1'], 'contains': ['432.da1', '432.db1', '432.dd1', '432.ea1', '432.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 43926348, 36933, 87265400268, 87124129], 'label': '6912.ia.216.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gm1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566148
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hl1', '108.bd1', '108.bp1', '108.cw1', '108.dc1', '108.ds1', '108.eh1', '108.fz1'], 'contains': ['432.da1', '432.df1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 87265400268], 'label': '6912.ia.216.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gn1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566149
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hm1', '108.bd1', '108.bx1', '108.cs1', '108.df1', '108.dk1', '108.ee1', '108.gd1'], 'contains': ['432.da1', '432.di1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.216.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.go1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566150
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hn1', '108.y1', '108.bk1', '108.dg1', '108.eb1', '108.ei1', '108.en1', '108.fr1'], 'contains': ['432.db1', '432.dc1', '432.de1', '432.ee1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87218588748, 36933, 87124129, 83480268], 'label': '6912.ia.216.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gp1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566151
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1', '9.c1'], 'contains': ['36.bv1', '36.bw1', '36.ca1', '36.cb1', '36.dx1', '36.dy1', '36.ex1', '36.ey1', '36.gy1', '36.ha1', '36.hc1', '36.hr1', '36.ht1', '36.iy1', '36.ja1', '54.x1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 40279680, 127370880, 87265400268, 93405312000, 127380345, 7620480], 'label': '6912.ia.18.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bq1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566152
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ho1', '108.w1', '108.bh1', '108.dj1', '108.ec1', '108.eh1', '108.en1', '108.fs1'], 'contains': ['432.db1', '432.dj1', '432.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222236613, 36933, 87100665, 87298060748], 'label': '6912.ia.216.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566153
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hp1', '108.x1', '108.bi1', '108.dh1', '108.ed1', '108.ei1', '108.em1', '108.fs1'], 'contains': ['432.db1', '432.dk1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222236613, 36933, 87100665, 87261772748], 'label': '6912.ia.216.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566154
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hq1', '108.w1', '108.bi1', '108.df1', '108.eb1', '108.el1', '108.eo1', '108.ft1'], 'contains': ['432.db1', '432.dl1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222236613, 36933, 87100665, 119769548], 'label': '6912.ia.216.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566155
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hr1', '108.x1', '108.bh1', '108.dg1', '108.ea1', '108.ej1', '108.ep1', '108.ft1'], 'contains': ['432.db1', '432.dm1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222236613, 36933, 87100665, 83481548], 'label': '6912.ia.216.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566156
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ic1', '108.y1', '108.bj1', '108.dh1', '108.ec1', '108.ej1', '108.eo1', '108.fu1'], 'contains': ['432.db1', '432.dg1', '432.dr1', '432.dx1', '432.dz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 40297548, 87222199680, 36933], 'label': '6912.ia.216.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ht1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.he1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566157
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hu1', '108.ba1', '108.br1', '108.cv1', '108.di1', '108.dt1', '108.eh1', '108.ga1'], 'contains': ['432.dd1', '432.df1', '432.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 36933, 87100665], 'label': '6912.ia.216.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.hu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gw1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566158
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hv1', '108.ba1', '108.bz1', '108.cr1', '108.df1', '108.dl1', '108.ek1', '108.ge1'], 'contains': ['432.dd1', '432.di1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 119768268, 87222200426, 36933, 87100665], 'label': '6912.ia.216.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gx1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566159
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hs1', '108.z1', '108.bs1', '108.cu1', '108.de1', '108.ds1', '108.ei1', '108.ga1'], 'contains': ['432.dc1', '432.df1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 83480268], 'label': '6912.ia.216.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.hw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gu1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566160
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ht1', '108.z1', '108.ca1', '108.cq1', '108.dg1', '108.dk1', '108.eg1', '108.ge1'], 'contains': ['432.dc1', '432.di1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222200426, 36933, 87100665, 83480268], 'label': '6912.ia.216.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gv1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566161
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hw1', '108.bb1', '108.bq1', '108.cx1', '108.dd1', '108.dt1', '108.ei1', '108.fz1'], 'contains': ['432.de1', '432.df1', '432.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 87305679948], 'label': '6912.ia.216.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gy1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566162
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.x1', '6.ba1', '9.c1'], 'contains': ['36.bx1', '36.by1', '36.cc1', '36.cd1', '36.dz1', '36.ed1', '36.ez1', '36.fa1', '36.gy1', '36.hb1', '36.hd1', '36.hs1', '36.hu1', '36.iz1', '36.jb1', '54.y1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.18.br1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.br1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243566163
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hx1', '108.bb1', '108.by1', '108.ct1', '108.dg1', '108.dl1', '108.ef1', '108.gd1'], 'contains': ['432.de1', '432.di1', '432.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.216.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gz1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566164
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hy1', '108.z1', '108.bp1', '108.cv1', '108.dd1', '108.dv1', '108.ej1', '108.gb1'], 'contains': ['432.df1', '432.dg1', '432.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665, 87261771468], 'label': '6912.ia.216.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ia1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ha1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566165
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hz1', '108.ba1', '108.bq1', '108.cu1', '108.dc1', '108.du1', '108.el1', '108.gb1'], 'contains': ['432.df1', '432.dh1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 43909226, 36933, 87100665], 'label': '6912.ia.216.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ib1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566166
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ia1', '108.z1', '108.bx1', '108.cr1', '108.dh1', '108.dn1', '108.ef1', '108.gf1'], 'contains': ['432.dg1', '432.di1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222200426, 36933, 87100665, 87261771468], 'label': '6912.ia.216.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ic1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hc1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566167
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ib1', '108.ba1', '108.by1', '108.cq1', '108.dj1', '108.dm1', '108.ee1', '108.gf1'], 'contains': ['432.dh1', '432.di1', '432.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87298059468, 9465, 87222200426, 36933, 87100665], 'label': '6912.ia.216.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.id1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566168
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.id1', '108.bb1', '108.br1', '108.cw1', '108.de1', '108.du1', '108.ej1', '108.gc1'], 'contains': ['432.df1', '432.dm1', '432.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 40297548, 36933], 'label': '6912.ia.216.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ie1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hf1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566169
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ie1', '108.bb1', '108.bz1', '108.cs1', '108.dh1', '108.dm1', '108.eg1', '108.gg1'], 'contains': ['432.di1', '432.dp1', '432.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 87222200426, 40297548, 36933], 'label': '6912.ia.216.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.if1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hg1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566170
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.if1', '72.il1', '72.ip1', '108.bc1', '108.cl1', '108.di1', '108.dz1', '108.ek1', '108.et1', '108.fj1'], 'contains': ['432.cz1', '432.dd1', '432.ds1'], 'core': '864.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.216.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.ig1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566171
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ig1', '72.im1', '108.bc1', '108.bk1', '108.dj1', '108.ed1', '108.el1', '108.ep1', '108.fu1'], 'contains': ['432.db1', '432.dh1', '432.ds1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87222199680, 36933, 87124129, 87109068], 'label': '6912.ia.216.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.ih1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566172
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ih1', '72.in1', '108.bd1', '108.bs1', '108.cx1', '108.di1', '108.dv1', '108.el1', '108.gc1'], 'contains': ['432.df1', '432.dn1', '432.ds1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43909226, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.216.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.ii1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hj1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566173
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.x1', '9.a1'], 'contains': ['36.c1', '36.bz1', '36.ce1', '36.eg1', '36.ff1', '36.he1', '36.jc1', '54.y1', '72.jg1'], 'core': '36.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.bs1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bs1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566174
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ii1', '72.io1', '72.iq1', '108.bd1', '108.ca1', '108.ct1', '108.dj1', '108.dn1', '108.ek1', '108.gg1'], 'contains': ['432.di1', '432.dq1', '432.ds1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.216.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ij1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hk1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566175
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ij1', '108.y1', '108.ck1', '108.fg1'], 'contains': ['432.du1', '432.dt1', '432.dv1', '432.dw1', '432.eb1', '432.dz1', '432.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 87218603809, 40297548, 36933, 119750400], 'label': '6912.ia.216.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.ik1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hl1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566176
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ik1', '108.y1', '108.bj1', '108.fr1'], 'contains': ['432.ea1', '432.dw1', '432.eb1', '432.dx1', '432.ee1', '432.dy1', '432.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 87218603809, 40297548, 36933, 83495329], 'label': '6912.ia.216.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.il1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566177
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jf1', '72.jg1', '72.jm1', '108.eu1', '108.fd1', '108.fe1'], 'contains': ['432.l1', '432.m1', '432.bh1', '432.bv1', '432.ei1', '432.ej1', '432.em1', '432.ke1', '432.kt1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 36933, 40279680], 'label': '6912.ia.216.hs1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '216.im1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566178
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jh1', '72.ji1', '72.jj1', '72.jn1', '108.eu1', '108.fd1', '108.ff1'], 'contains': ['432.n1', '432.o1', '432.cf1', '432.cr1', '432.ei1', '432.el1', '432.en1', '432.kf1', '432.ku1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 127370880, 87222200426, 36933, 40279680], 'label': '6912.ia.216.ht1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.in1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ht1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566179
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jk1', '72.jo1', '108.ev1', '108.fe1', '108.ff1', '108.fg1', '108.fh1', '108.fi1', '108.fj1'], 'contains': ['432.p1', '432.q1', '432.cz1', '432.dt1', '432.ei1', '432.eo1', '432.eq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 36933, 40279680], 'label': '6912.ia.216.hu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.io1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566180
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jl1', '72.jp1', '108.ev1', '108.fd1', '108.fg1'], 'contains': ['432.r1', '432.s1', '432.du1', '432.dv1', '432.ei1', '432.ep1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 87218603809, 36933, 40279680], 'label': '6912.ia.216.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ip1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566181
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jq1', '72.jr1', '72.js1', '72.kd1', '108.eu1', '108.fk1', '108.fl1'], 'contains': ['432.bc1', '432.bi1', '432.bn1', '432.by1', '432.ej1', '432.ek1', '432.en1', '432.kg1', '432.kv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87185911680, 87222200426, 36933, 40279680], 'label': '6912.ia.216.hw1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.iq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566182
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jt1', '72.ju1', '108.ex1', '108.fd1', '108.fk1'], 'contains': ['432.bd1', '432.bf1', '432.bu1', '432.bx1', '432.ej1', '432.el1', '432.ep1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40280426, 36933, 87305671545, 40279680], 'label': '6912.ia.216.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '216.ir1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566183
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jv1', '72.jw1', '108.ew1', '108.fe1', '108.fk1'], 'contains': ['432.be1', '432.bj1', '432.bw1', '432.ca1', '432.ej1', '432.em1', '432.eq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 36933, 40279680], 'label': '6912.ia.216.hy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '216.is1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566184
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bb1', '9.c1'], 'contains': ['36.cf1', '36.cg1', '36.cl1', '36.cm1', '36.fh1', '36.fi1', '36.fx1', '36.fy1', '36.gz1', '36.ha1', '36.hb1', '36.is1', '36.iu1', '36.ji1', '36.jk1', '54.z1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.18.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bt1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566185
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jx1', '72.jy1', '72.jz1', '108.ew1', '108.fd1', '108.fl1'], 'contains': ['432.bg1', '432.bk1', '432.bz1', '432.cb1', '432.ej1', '432.en1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 127370880, 87222200426, 36933, 40279680], 'label': '6912.ia.216.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.it1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566186
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ka1', '72.kb1', '72.kc1', '108.ex1', '108.fe1', '108.fl1', '108.fm1', '108.fn1', '108.fo1', '108.fp1'], 'contains': ['432.bl1', '432.bm1', '432.cc1', '432.ej1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 36933, 40279680], 'label': '6912.ia.216.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '216.iu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ia1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566187
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ke1', '72.kf1', '72.kg1', '108.eu1', '108.fk1', '108.fq1'], 'contains': ['432.bo1', '432.bp1', '432.cg1', '432.cl1', '432.ek1', '432.el1', '432.em1', '432.kh1', '432.kw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 36933, 40279680], 'label': '6912.ia.216.ib1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.iv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ib1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566188
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kh1', '72.kj1', '72.kl1', '108.ev1', '108.fl1', '108.fq1', '108.fr1', '108.fs1', '108.ft1', '108.fu1'], 'contains': ['432.bq1', '432.br1', '432.db1', '432.dx1', '432.ek1', '432.eo1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 36933, 40279680], 'label': '6912.ia.216.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.iw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ic1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566189
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ki1', '72.kk1', '108.ev1', '108.fk1', '108.fr1'], 'contains': ['432.bs1', '432.bt1', '432.ea1', '432.ee1', '432.ek1', '432.ep1', '432.eq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 127370880, 87218603809, 36933, 40279680], 'label': '6912.ia.216.id1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ix1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.id1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566190
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.km1', '72.kp1', '108.ew1', '108.fd1', '108.fq1'], 'contains': ['432.cd1', '432.ci1', '432.cm1', '432.cu1', '432.el1', '432.em1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 127370880, 43909226, 36933, 40279680], 'label': '6912.ia.216.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.iy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ie1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566191
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kn1', '72.kq1', '108.ew1', '108.ff1', '108.fk1'], 'contains': ['432.ce1', '432.ch1', '432.cs1', '432.ct1', '432.el1', '432.en1', '432.eq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 119759865, 87222200426, 36933, 40279680], 'label': '6912.ia.216.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.iz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.if1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566192
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ko1', '72.kr1', '108.ex1', '108.ff1', '108.fq1', '108.fv1', '108.fw1', '108.fx1', '108.fy1'], 'contains': ['432.cj1', '432.ck1', '432.cv1', '432.el1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87218571626, 36933, 40279680], 'label': '6912.ia.216.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.ja1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ig1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566193
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ks1', '72.ku1', '108.ey1', '108.fd1', '108.fk1'], 'contains': ['432.cn1', '432.cp1', '432.cx1', '432.ed1', '432.em1', '432.en1', '432.ep1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 43909226, 36933, 87305671545, 40279680], 'label': '6912.ia.216.ih1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '216.jb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ih1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566194
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kt1', '72.kv1', '108.ey1', '108.fe1', '108.fq1', '108.fz1', '108.ga1', '108.gb1', '108.gc1'], 'contains': ['432.co1', '432.cq1', '432.df1', '432.em1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 36933, 40279680], 'label': '6912.ia.216.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.jc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ii1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566195
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1', '6.bc1', '9.c1'], 'contains': ['36.ch1', '36.ci1', '36.cn1', '36.co1', '36.fj1', '36.fn1', '36.fz1', '36.ga1', '36.gz1', '36.hc1', '36.hd1', '36.it1', '36.iv1', '36.jj1', '36.jl1', '54.ba1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.18.bu1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bu1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566196
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kw1', '72.kx1', '72.ky1', '108.ey1', '108.ff1', '108.fl1', '108.gd1', '108.ge1', '108.gf1', '108.gg1'], 'contains': ['432.cw1', '432.cy1', '432.di1', '432.en1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 36933, 40279680], 'label': '6912.ia.216.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ij1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566197
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kz1', '72.lh1', '108.fc1', '108.fg1', '108.fm1', '108.fr1', '108.fv1', '108.fz1', '108.gd1'], 'contains': ['432.da1', '432.de1', '432.dw1', '432.eo1', '432.ep1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 87265400268, 40279680], 'label': '6912.ia.216.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.je1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ik1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566198
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.la1', '72.li1', '108.ez1', '108.fj1', '108.fn1', '108.fr1', '108.fw1', '108.ga1', '108.ge1'], 'contains': ['432.dd1', '432.dc1', '432.dy1', '432.eo1', '432.eq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 83480268, 40279680], 'label': '6912.ia.216.il1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.jf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.il1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566199
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lb1', '72.lj1', '72.lq1', '108.ez1', '108.fg1', '108.fo1', '108.fu1', '108.fx1', '108.gb1', '108.gf1'], 'contains': ['432.dg1', '432.dh1', '432.dz1', '432.eo1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 87261771468, 40279680], 'label': '6912.ia.216.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.im1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243566200
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lc1', '72.lk1', '72.lr1', '108.fa1', '108.fh1', '108.fp1', '108.fs1', '108.fv1', '108.ga1', '108.gf1'], 'contains': ['432.dj1', '432.dk1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 36933, 40279680], 'label': '6912.ia.216.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '216.jh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.in1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566201
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ld1', '72.ll1', '108.fa1', '108.fi1', '108.fm1', '108.ft1', '108.fy1', '108.gb1', '108.ge1'], 'contains': ['432.dl1', '432.do1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305681228, 127370880, 127380345, 36933, 40279680], 'label': '6912.ia.216.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.ji1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.io1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566202
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.le1', '72.lm1', '108.fb1', '108.fh1', '108.fn1', '108.ft1', '108.fx1', '108.gc1', '108.gd1'], 'contains': ['432.dm1', '432.dn1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 119769548, 40279680], 'label': '6912.ia.216.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '216.jj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ip1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566203
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lf1', '72.ln1', '72.ls1', '108.fb1', '108.fi1', '108.fo1', '108.fs1', '108.fw1', '108.fz1', '108.gg1'], 'contains': ['432.dp1', '432.dq1', '432.eo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87298060748, 40279680], 'label': '6912.ia.216.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566204
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lg1', '72.lo1', '108.ez1', '108.fg1', '108.fr1'], 'contains': ['432.ec1', '432.eb1', '432.eg1', '432.ef1', '432.ep1', '432.eq1', '432.er1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87218603809, 36933, 83480268, 40279680], 'label': '6912.ia.216.ir1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '216.jl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ir1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566205
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ne1', '108.b1'], 'contains': ['432.fn1', '432.fo1', '432.fq1', '432.fr1', '432.fs1', '432.fw1', '432.fy1', '432.gk1', '432.gm1', '432.go1', '432.gu1', '432.hg1', '432.hh1', '432.hr1', '432.ht1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 7656719, 36933, 87265419333, 87100665], 'label': '6912.ia.216.jm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '216.jm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566206
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1', '6.bd1', '9.a1'], 'contains': ['36.cj1', '36.cp1', '36.fp1', '36.gb1', '36.he1', '36.iw1', '36.jm1', '54.ba1', '72.ji1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.bv1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bv1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566207
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nf1', '108.b1', '108.gl1', '108.gm1'], 'contains': ['432.fn1', '432.fp1', '432.ft1', '432.fu1', '432.ga1', '432.gm1', '432.gn1', '432.gt1', '432.hi1', '432.hj1', '432.hv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 7621226, 36933, 87265419333], 'label': '6912.ia.216.jn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566208
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ng1', '108.b1', '108.gn1', '108.go1'], 'contains': ['432.fo1', '432.fp1', '432.fv1', '432.fx1', '432.fz1', '432.go1', '432.gq1', '432.gt1', '432.hq1', '432.hs1', '432.hu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87265419333, 83498639], 'label': '6912.ia.216.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jo1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566209
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nh1', '108.g1', '108.gl1', '108.gn1'], 'contains': ['432.fp1', '432.fq1', '432.gc1', '432.gb1', '432.gj1', '432.gv1', '432.gx1', '432.hd1', '432.hx1', '432.hw1', '432.ie1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87100665, 87124129, 87265382400], 'label': '6912.ia.216.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566210
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ni1', '108.d1', '108.gm1', '108.gn1'], 'contains': ['432.fp1', '432.ge1', '432.gh1', '432.gy1', '432.hb1', '432.hz1', '432.ic1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 7654690, 36933, 87265419333], 'label': '6912.ia.216.jq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566211
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nj1', '108.d1', '108.gl1', '108.go1'], 'contains': ['432.fp1', '432.gf1', '432.gg1', '432.gz1', '432.hb1', '432.ia1', '432.ib1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87265419333, 83496610], 'label': '6912.ia.216.jr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jr1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566212
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nd1', '72.nk1', '108.g1', '108.gm1', '108.go1'], 'contains': ['432.fp1', '432.gd1', '432.gi1', '432.gx1', '432.hc1', '432.hy1', '432.id1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 87265382400], 'label': '6912.ia.216.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.js1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.js1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566213
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nm1', '72.oh1', '108.gi1', '108.bl1', '108.gl1'], 'contains': ['432.fu1', '432.gc1', '432.gg1', '432.hl1', '432.ho1', '432.iw1', '432.ja1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 7621226, 36933], 'label': '6912.ia.216.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ju1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566214
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nl1', '108.gh1', '108.bo1', '108.gl1'], 'contains': ['432.fu1', '432.gb1', '432.gf1', '432.hk1', '432.hm1', '432.iv1', '432.iy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.216.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '216.ju1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jt1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566215
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nn1', '108.gh1', '108.bl1', '108.gm1'], 'contains': ['432.fu1', '432.gd1', '432.gh1', '432.hn1', '432.ho1', '432.iz1', '432.jb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 7621226, 36933, 87265415329], 'label': '6912.ia.216.jv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566216
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.no1', '72.np1', '72.oi1', '108.gi1', '108.bo1', '108.gm1'], 'contains': ['432.fu1', '432.ge1', '432.gi1', '432.hm1', '432.hp1', '432.ix1', '432.jc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 7621226, 36933], 'label': '6912.ia.216.jw1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '216.jw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566217
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1', '6.be1'], 'contains': ['36.ck1', '36.cq1', '36.fr1', '36.gc1', '36.hf1', '36.ix1', '36.jr1', '54.ba1', '72.jj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87222200426, 36933, 93405314676, 87109068, 40279680], 'label': '6912.ia.18.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '18.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bw1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566218
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nr1', '108.gk1', '108.bl1', '108.gn1'], 'contains': ['432.fx1', '432.gc1', '432.gh1', '432.ih1', '432.il1', '432.iw1', '432.jb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 36933, 83498639], 'label': '6912.ia.216.jy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jy1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566219
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nq1', '108.gj1', '108.bo1', '108.gn1'], 'contains': ['432.fx1', '432.gb1', '432.ge1', '432.if1', '432.ii1', '432.iv1', '432.ix1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.216.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '216.jy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566220
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ns1', '108.gj1', '108.bl1', '108.go1'], 'contains': ['432.fx1', '432.gd1', '432.gg1', '432.ij1', '432.il1', '432.iz1', '432.ja1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 83498639, 87265415329], 'label': '6912.ia.216.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.jz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566221
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nt1', '72.nu1', '108.gk1', '108.bo1', '108.go1'], 'contains': ['432.fx1', '432.gf1', '432.gi1', '432.ii1', '432.im1', '432.iy1', '432.jc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 83463146], 'label': '6912.ia.216.ka1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '216.ka1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ka1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566222
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nw1', '72.oj1', '108.gi1', '108.bt1', '108.gn1'], 'contains': ['432.fz1', '432.gc1', '432.ge1', '432.iq1', '432.it1', '432.jq1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 7654690, 36933], 'label': '6912.ia.216.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566223
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nv1', '108.gh1', '108.bw1', '108.gn1'], 'contains': ['432.fz1', '432.gb1', '432.gh1', '432.ip1', '432.ir1', '432.jp1', '432.js1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.216.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566224
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nx1', '108.gh1', '108.bt1', '108.go1'], 'contains': ['432.fz1', '432.gd1', '432.gf1', '432.is1', '432.it1', '432.jt1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 83496610, 87265415329], 'label': '6912.ia.216.kd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566225
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ny1', '72.nz1', '72.oa1', '72.ok1', '108.gi1', '108.bw1', '108.go1'], 'contains': ['432.fz1', '432.gg1', '432.gi1', '432.ir1', '432.iu1', '432.jr1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 87185912426], 'label': '6912.ia.216.ke1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ke1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ke1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566226
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oc1', '108.gk1', '108.bt1', '108.gl1'], 'contains': ['432.ga1', '432.gc1', '432.gf1', '432.jh1', '432.jl1', '432.jq1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 87178324129, 36933, 83496610], 'label': '6912.ia.216.kg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kg1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566227
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ob1', '108.gj1', '108.bw1', '108.gl1'], 'contains': ['432.ga1', '432.gb1', '432.gg1', '432.jf1', '432.ji1', '432.jp1', '432.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.216.kf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kf1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566228
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.f1', '12.bm1', '12.cx1', '18.bd1', '18.be1', '24.bc1', '24.db1'], 'core': '12.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 40280426, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.m1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243566229
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1', '9.b1'], 'contains': ['36.hh1', '36.hj1', '36.hl1', '36.hv1', '36.hx1', '36.jd1', '36.jf1', '54.x1', '72.oh1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.18.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bx1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566230
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.od1', '108.gj1', '108.bt1', '108.gm1'], 'contains': ['432.ga1', '432.gd1', '432.ge1', '432.jj1', '432.jl1', '432.jt1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 7654690, 36933, 87265415329], 'label': '6912.ia.216.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566231
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oe1', '72.of1', '72.og1', '108.gk1', '108.bw1', '108.gm1'], 'contains': ['432.ga1', '432.gh1', '432.gi1', '432.ji1', '432.jm1', '432.js1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 87261754346], 'label': '6912.ia.216.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ki1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ki1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566232
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.op1', '108.m1', '108.cf1', '108.gl1'], 'contains': ['432.gn1', '432.gv1', '432.gz1', '432.hl1', '432.hk1', '432.jh1', '432.jf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 36933, 746], 'label': '6912.ia.216.kj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.kj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566233
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oq1', '108.l1', '108.cf1', '108.cg1'], 'contains': ['432.gn1', '432.gw1', '432.ha1', '432.hk1', '432.hn1', '432.jg1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 36933, 746, 87265382400], 'label': '6912.ia.216.kk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.kk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566234
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.or1', '108.j1', '108.gl1', '108.gm1'], 'contains': ['432.gn1', '432.gx1', '432.hb1', '432.hm1', '432.ho1', '432.ji1', '432.jl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87265419333, 83495329, 83496610], 'label': '6912.ia.216.kl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kl1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566235
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ol1', '72.os1', '108.m1', '108.cg1', '108.gm1'], 'contains': ['432.gn1', '432.gy1', '432.hc1', '432.hn1', '432.hp1', '432.jj1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933, 746], 'label': '6912.ia.216.km1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.km1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.km1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566236
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ot1', '108.m1', '108.co1', '108.gn1'], 'contains': ['432.gq1', '432.gv1', '432.gy1', '432.ih1', '432.if1', '432.iq1', '432.ip1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 36933, 127371626], 'label': '6912.ia.216.kn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.kn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566237
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ou1', '108.l1', '108.co1', '108.cp1'], 'contains': ['432.gq1', '432.gw1', '432.ha1', '432.ig1', '432.ik1', '432.ip1', '432.is1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 36933, 87091946, 87265382400], 'label': '6912.ia.216.ko1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.ko1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ko1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566238
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ov1', '108.j1', '108.gn1', '108.go1'], 'contains': ['432.gq1', '432.gx1', '432.hb1', '432.ii1', '432.il1', '432.ir1', '432.it1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7654690, 36933, 87265419333, 83495329], 'label': '6912.ia.216.kp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566239
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.om1', '72.ow1', '108.m1', '108.cp1', '108.go1'], 'contains': ['432.gq1', '432.gz1', '432.hc1', '432.ij1', '432.im1', '432.is1', '432.iu1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 40280426, 36933], 'label': '6912.ia.216.kq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.kq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566240
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.ba1', '9.b1'], 'contains': ['36.b1', '36.hh1', '36.hk1', '36.hw1', '36.hy1', '36.je1', '36.jg1', '54.y1', '72.oi1'], 'core': '36.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.by1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.by1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566241
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ox1', '108.r1', '108.cf1', '108.co1'], 'contains': ['432.gr1', '432.gv1', '432.ha1', '432.ih1', '432.ig1', '432.jh1', '432.jg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 87305662080, 40280426, 36933], 'label': '6912.ia.216.kr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.kr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kr1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566242
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oy1', '108.q1', '108.cg1', '108.co1'], 'contains': ['432.gr1', '432.gw1', '432.gy1', '432.if1', '432.ik1', '432.jg1', '432.jj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 36933, 127371626, 87265382400], 'label': '6912.ia.216.ks1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.ks1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ks1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566243
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oz1', '108.q1', '108.cf1', '108.cp1'], 'contains': ['432.gr1', '432.gw1', '432.gz1', '432.ig1', '432.ij1', '432.jf1', '432.jk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 40280426, 36933, 87265382400], 'label': '6912.ia.216.kt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.kt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kt1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566244
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.on1', '72.pa1', '108.r1', '108.cg1', '108.cp1'], 'contains': ['432.gr1', '432.ha1', '432.hc1', '432.ik1', '432.im1', '432.jk1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933, 127371626], 'label': '6912.ia.216.ku1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '216.ku1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ku1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566245
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pb1', '108.o1'], 'contains': ['432.gs1', '432.hd1', '432.he1', '432.in1', '432.io1', '432.jn1', '432.jo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7653409, 43942690, 36933, 87265419333, 87100665], 'label': '6912.ia.216.kv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1', 'old_label': '216.kv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566246
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pc1', '108.v1', '108.gl1', '108.gn1'], 'contains': ['432.gt1', '432.gv1', '432.hb1', '432.iw1', '432.iv1', '432.jq1', '432.jp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 83463146, 87124129, 87109068, 87265382400], 'label': '6912.ia.216.kw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566247
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pd1', '108.s1', '108.gm1', '108.gn1'], 'contains': ['432.gt1', '432.gx1', '432.gy1', '432.ix1', '432.jb1', '432.js1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87265419333, 83498639, 83495329], 'label': '6912.ia.216.kx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566248
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pe1', '108.s1', '108.gl1', '108.go1'], 'contains': ['432.gt1', '432.gx1', '432.gz1', '432.iy1', '432.ja1', '432.jr1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7621226, 36933, 87265419333, 83495329], 'label': '6912.ia.216.ky1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ky1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ky1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566249
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oo1', '72.pf1', '108.v1', '108.gm1', '108.go1'], 'contains': ['432.gt1', '432.hb1', '432.hc1', '432.iz1', '432.jc1', '432.jt1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 32929, 7621226, 36933, 87265382400], 'label': '6912.ia.216.kz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.kz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566250
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pg1', '108.u1'], 'contains': ['432.gu1', '432.he1', '432.hf1', '432.jd1', '432.je1', '432.jx1', '432.jy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40297548, 36933, 87100665, 83463146, 87265382400], 'label': '6912.ia.216.la1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.u1', 'old_label': '216.la1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.la1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566251
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bb1', '9.b1'], 'contains': ['36.hi1', '36.hj1', '36.hk1', '36.io1', '36.iq1', '36.jn1', '36.jp1', '54.z1', '72.oj1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 47537280, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.18.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bz1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566252
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pi1', '72.pl1', '108.gi1', '108.cy1', '108.gl1'], 'contains': ['432.hj1', '432.hl1', '432.hm1', '432.hx1', '432.ib1', '432.jq1', '432.jr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 36933, 83495329, 83496610], 'label': '6912.ia.216.lc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566253
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ph1', '108.gh1', '108.db1', '108.gl1'], 'contains': ['432.hj1', '432.hk1', '432.ho1', '432.hw1', '432.ia1', '432.jp1', '432.jv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.216.lb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566254
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pj1', '108.gh1', '108.cy1', '108.gm1'], 'contains': ['432.hj1', '432.hm1', '432.hn1', '432.hy1', '432.ic1', '432.js1', '432.jt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83495329, 83496610, 87265415329], 'label': '6912.ia.216.ld1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ld1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ld1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566255
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pk1', '72.pm1', '72.pn1', '72.po1', '108.gi1', '108.db1', '108.gm1'], 'contains': ['432.hj1', '432.ho1', '432.hp1', '432.hz1', '432.id1', '432.ju1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 87185912426], 'label': '6912.ia.216.le1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.le1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.le1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566256
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pt1', '108.gk1', '108.cy1', '108.gn1'], 'contains': ['432.hs1', '432.hx1', '432.ic1', '432.ih1', '432.ii1', '432.jq1', '432.js1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 7654690, 36933, 83495329], 'label': '6912.ia.216.lg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lg1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566257
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ps1', '108.gj1', '108.db1', '108.gn1'], 'contains': ['432.hs1', '432.hw1', '432.hz1', '432.if1', '432.il1', '432.jp1', '432.ju1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.216.lf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lf1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566258
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pu1', '108.gj1', '108.cy1', '108.go1'], 'contains': ['432.hs1', '432.hy1', '432.ib1', '432.ii1', '432.ij1', '432.jr1', '432.jt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7654690, 36933, 83495329, 87265415329], 'label': '6912.ia.216.lh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566259
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pp1', '72.pv1', '108.gk1', '108.db1', '108.go1'], 'contains': ['432.hs1', '432.ia1', '432.id1', '432.il1', '432.im1', '432.jv1', '432.jw1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 87261754346], 'label': '6912.ia.216.li1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.li1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.li1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566260
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pw1', '72.pz1', '108.gi1', '108.do1', '108.gn1'], 'contains': ['432.hu1', '432.hx1', '432.hz1', '432.iq1', '432.ir1', '432.iw1', '432.ix1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 36933, 83498639, 83495329], 'label': '6912.ia.216.lk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566261
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.py1', '108.gh1', '108.dr1', '108.gn1'], 'contains': ['432.hu1', '432.hw1', '432.ic1', '432.ip1', '432.it1', '432.iv1', '432.jb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.216.lj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566262
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bc1', '6.bd1', '6.be1', '9.b1'], 'contains': ['36.b1', '36.hi1', '36.hl1', '36.ip1', '36.ir1', '36.jo1', '36.jq1', '54.ba1', '72.ok1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.ca1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ca1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566263
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.qa1', '108.gh1', '108.do1', '108.go1'], 'contains': ['432.hu1', '432.hy1', '432.ia1', '432.ir1', '432.is1', '432.iy1', '432.iz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7621226, 36933, 83495329, 87265415329], 'label': '6912.ia.216.ll1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ll1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ll1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566264
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pq1', '72.px1', '72.qb1', '108.gi1', '108.dr1', '108.go1'], 'contains': ['432.hu1', '432.ib1', '432.id1', '432.it1', '432.iu1', '432.ja1', '432.jc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 7621226, 36933], 'label': '6912.ia.216.lm1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lm1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566265
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.qd1', '108.gk1', '108.do1', '108.gl1'], 'contains': ['432.hv1', '432.hx1', '432.ia1', '432.iw1', '432.iy1', '432.jh1', '432.ji1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 7621226, 36933, 83495329], 'label': '6912.ia.216.lo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.ln1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lo1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566266
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.qc1', '108.gj1', '108.dr1', '108.gl1'], 'contains': ['432.hv1', '432.hw1', '432.ib1', '432.iv1', '432.ja1', '432.jf1', '432.jl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.216.ln1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ln1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566267
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.qe1', '108.gj1', '108.do1', '108.gm1'], 'contains': ['432.hv1', '432.hy1', '432.hz1', '432.ix1', '432.iz1', '432.ji1', '432.jj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83498639, 83495329, 87265415329], 'label': '6912.ia.216.lp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566268
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pr1', '72.qf1', '108.gk1', '108.dr1', '108.gm1'], 'contains': ['432.hv1', '432.ic1', '432.id1', '432.jb1', '432.jc1', '432.jl1', '432.jm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933, 83463146], 'label': '6912.ia.216.lq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '216.lq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566269
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.qg1', '72.qh1', '108.eu1'], 'contains': ['432.kb1', '432.kc1', '432.kd1', '432.ki1', '432.kj1', '432.kk1', '432.kl1', '432.ke1', '432.kf1', '432.kg1', '432.kh1', '432.kp1', '432.kq1', '432.kr1', '432.ks1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40316613, 87178291200, 7657413, 43944719, 127407813], 'label': '6912.ia.216.lr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '216.lr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.lr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566270
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '216.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.qi1', '72.qj1', '72.qk1', '108.eu1'], 'contains': ['432.ki1', '432.kj1', '432.kk1', '432.kl1', '432.km1', '432.kn1', '432.ko1', '432.kp1', '432.kq1', '432.kr1', '432.ks1', '432.kt1', '432.ku1', '432.kv1', '432.kw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [127370880, 7657413, 43944719, 87178328133, 40279680], 'label': '6912.ia.216.ls1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '216.ls1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ls1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566271
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1', '128.a1', '128.b1', '128.c1', '128.d1', '128.e1', '128.f1', '128.g1', '128.h1'], 'contains': ['768.a1', '768.b1', '768.c1', '768.d1', '768.e1', '768.f1', '768.g1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280], 'label': '6912.ia.256.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '256.a1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566289
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.hp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iy1', '96.bk1', '144.hj1', '144.hl1', '144.hm1', '144.ho1', '144.hp1', '144.hq1', '144.hr1'], 'contains': ['576.h1', '576.bx1', '576.by1', '864.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [32929, 87178291200, 47537280, 36933], 'label': '6912.ia.288.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566272
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.t1', '96.u1', '144.a1', '144.fw1', '144.fz1', '144.ge1', '144.gi1', '144.gl1', '144.gp1', '144.gw1', '144.gx1', '144.gy1', '144.gz1'], 'contains': ['576.b1', '576.d1', '576.dd1', '864.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 36933, 40279680], 'label': '6912.ia.288.a1', 'mobius_quo': -1, 'mobius_sub': 288, 'normal_closure': '288.a1', 'normal_contained_in': ['72.a1', '96.a1', '144.a1'], 'normal_contains': ['576.b1', '864.a1', '1152.a1'], 'normalizer': '1.a1', 'old_label': '288.a1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566273
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bf1', '9.c1'], 'contains': ['36.dt1', '36.du1', '36.ea1', '36.eb1', '36.el1', '36.em1', '36.fb1', '36.fc1', '36.ho1', '36.hr1', '36.hs1', '36.ie1', '36.ig1', '36.ji1', '36.jj1', '54.bb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87265400268, 83480268, 119769548, 40279680], 'label': '6912.ia.18.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cb1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566274
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.v1', '96.x1', '144.b1', '144.fu1', '144.ga1', '144.gf1', '144.gh1', '144.gn1', '144.gr1', '144.ha1', '144.hb1', '144.hc1', '144.hd1'], 'contains': ['576.c1', '864.a1', '1152.d1'], 'core': '288.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 47537280, 36933, 40279680], 'label': '6912.ia.288.b1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.b1', 'normal_contained_in': ['72.c1', '96.a1', '144.b1'], 'normal_contains': ['576.c1', '864.a1'], 'normalizer': '1.a1', 'old_label': '288.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566275
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': ['24.er1'], 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.de1', '96.dg1', '144.c1', '144.fc1', '144.jl1', '144.kp1', '144.lf1', '144.mb1', '144.mq1', '144.nd1', '144.nn1', '144.oe1', '144.oq1'], 'contains': ['576.br1', '864.b1'], 'core': '288.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933], 'label': '6912.ia.288.c1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.c1', 'normal_contained_in': ['72.a1', '96.b1', '144.c1'], 'normal_contains': ['864.b1', '1152.a1'], 'normalizer': '1.a1', 'old_label': '288.c1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '288.c1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566276
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': ['24.et1'], 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.di1', '96.dj1', '144.d1', '144.hn1', '144.fr1', '144.jn1', '144.jw1', '144.lm1', '144.mt1', '144.ne1', '144.nq1', '144.oh1', '144.ot1'], 'contains': ['864.b1', '1152.c1'], 'core': '288.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 32929, 36933, 2676], 'label': '6912.ia.288.d1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.d1', 'normal_contained_in': ['72.b1', '96.b1', '144.d1'], 'normal_contains': ['864.b1'], 'normalizer': '1.a1', 'old_label': '288.d1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566277
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': ['24.el1', '24.dw1', '24.dz1', '24.ea1', '24.ei1', '24.ej1'], 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.el1', '96.em1', '144.a1', '144.qm1', '144.qn1', '144.qo1'], 'contains': ['576.b1', '576.dp1', '576.dy1', '864.fb1'], 'core': '288.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 93405312000, 87178328133, 40279680], 'label': '6912.ia.288.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': ['96.c1', '144.a1'], 'normal_contains': ['576.b1', '1152.b1'], 'normalizer': '1.a1', 'old_label': '288.e1', 'projective_image': '6912.ia', 'quotient_action_image': '12.4', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '288.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566278
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': ['24.ee1', '24.dk1', '24.do1', '24.dn1', '24.em1', '24.en1', '24.ek1', '24.eh1', '24.ej1', '24.e1', '24.ec1', '24.dj1', '24.eb1', '24.ed1'], 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '96.fn1', '96.fo1', '144.b1', '144.qc1', '144.rc1', '144.rd1'], 'contains': ['576.c1', '864.ga1', '1152.u1'], 'core': '288.f1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 7657413, 47537280, 40279680], 'label': '6912.ia.288.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '288.f1', 'normal_contained_in': ['96.d1', '144.b1'], 'normal_contains': ['576.c1'], 'normalizer': '1.a1', 'old_label': '288.f1', 'projective_image': '6912.ia', 'quotient_action_image': '4.2', 'quotient_action_kernel': '72.25', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '288.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566279
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ir1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '96.f1', '144.e1', '144.f1', '144.g1', '144.h1', '144.i1', '144.j1', '144.ft1'], 'contains': ['576.g1', '576.e1', '576.n1', '576.dg1', '576.cd1', '864.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178291200, 36933, 2676, 40279680], 'label': '6912.ia.288.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566280
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lw1', '96.z1', '96.bc1', '144.e1', '144.hg1', '144.hh1'], 'contains': ['576.g1', '576.k1', '576.t1', '576.dh1', '864.y1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 2676], 'label': '6912.ia.288.cb1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566281
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.is1', '96.z1', '96.bd1', '144.hi1', '144.hj1'], 'contains': ['576.h1', '576.m1', '576.v1', '576.di1', '864.y1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 87178291200, 47537280, 36933], 'label': '6912.ia.288.cc1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '288.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566282
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.it1', '96.ba1', '96.be1', '144.hi1', '144.hk1', '144.hl1'], 'contains': ['576.h1', '576.q1', '576.z1', '576.dj1', '864.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178291200, 47537280, 36933, 746], 'label': '6912.ia.288.cd1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566283
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.mc1', '96.ba1', '96.bf1', '144.f1', '144.hg1'], 'contains': ['576.g1', '576.s1', '576.bb1', '576.dk1', '864.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87178291200, 36933, 746, 2676], 'label': '6912.ia.288.ce1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '288.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566284
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bg1', '6.bh1', '9.c1'], 'contains': ['36.dv1', '36.dw1', '36.ec1', '36.ee1', '36.en1', '36.eo1', '36.fd1', '36.fe1', '36.ho1', '36.ht1', '36.hu1', '36.if1', '36.ih1', '36.jk1', '36.jl1', '54.bc1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.18.cc1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566285
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.md1', '96.bg1', '144.f1', '144.g1', '144.hh1'], 'contains': ['576.g1', '576.y1', '576.bi1', '576.dl1', '864.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40280426, 87178291200, 36933, 2676], 'label': '6912.ia.288.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566286
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.me1', '96.bb1', '96.bh1', '144.h1', '144.hg1', '144.hh1'], 'contains': ['576.g1', '576.be1', '576.bl1', '576.dm1', '864.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6851, 87178291200, 36933, 83468087], 'label': '6912.ia.288.cg1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566287
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iw1', '96.bb1', '96.bi1', '144.hi1', '144.hk1', '144.hm1'], 'contains': ['576.h1', '576.bf1', '576.bm1', '576.dn1', '864.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178291200, 79833600, 36933, 83468087], 'label': '6912.ia.288.ch1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566291
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '144.a1', '144.k1', '144.l1', '144.m1', '144.n1', '144.o1', '144.p1', '144.q1', '144.s1', '144.r1', '144.t1'], 'contains': ['576.a1', '576.d1', '576.o1', '576.dp1', '576.ce1', '864.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.288.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566292
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1', '96.bd1', '144.k1', '144.hu1', '144.hv1', '144.hw1', '144.hx1'], 'contains': ['576.a1', '576.j1', '576.u1', '576.dq1', '864.y1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933], 'label': '6912.ia.288.cl1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '288.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566293
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.be1', '96.bf1', '144.l1', '144.hu1', '144.hy1', '144.hz1', '144.ia1'], 'contains': ['576.a1', '576.p1', '576.ba1', '576.dr1', '864.z1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 746], 'label': '6912.ia.288.cm1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '288.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566294
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '144.l1', '144.m1', '144.hv1', '144.hy1', '144.ib1', '144.ic1', '144.id1'], 'contains': ['576.a1', '576.x1', '576.bh1', '576.ds1', '864.ba1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 87178291200, 36933], 'label': '6912.ia.288.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566295
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bf1', '9.b1'], 'contains': ['36.hp1', '36.hv1', '36.hw1', '36.ii1', '36.ik1', '36.jn1', '36.jo1', '54.bb1', '72.pl1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87265400268, 83480268, 119769548, 40279680], 'label': '6912.ia.18.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cd1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566296
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1', '96.bi1', '96.bj1', '144.n1', '144.hu1', '144.hv1', '144.hz1', '144.ib1', '144.ie1', '144.if1'], 'contains': ['576.a1', '576.bd1', '576.bk1', '576.dt1', '864.bb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 83468087], 'label': '6912.ia.288.co1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566297
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1', '144.c1', '144.o1', '144.hw1', '144.ia1', '144.ic1', '144.ie1', '144.ig1', '144.ih1', '144.ii1', '144.ij1', '144.ik1'], 'contains': ['576.a1', '576.br1', '576.bt1', '864.bc1'], 'core': '576.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.288.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566298
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.q1', '144.hx1', '144.hy1', '144.id1', '144.if1', '144.ig1', '144.il1', '144.im1', '144.in1'], 'contains': ['576.a1', '576.bs1', '576.bv1', '864.bd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 87178291200, 127403809, 36933], 'label': '6912.ia.288.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566299
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bl1', '144.r1', '144.hw1', '144.hx1', '144.hz1', '144.ib1', '144.ih1', '144.il1'], 'contains': ['576.a1', '576.bu1', '576.bw1', '864.be1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 83495329], 'label': '6912.ia.288.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566300
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1', '144.k1', '144.v1', '144.w1', '144.y1', '144.ba1', '144.bd1', '144.bg1', '144.bi1', '144.bh1', '144.bj1', '144.fw1'], 'contains': ['576.d1', '576.j1', '576.du1', '576.cf1', '864.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87091200], 'label': '6912.ia.288.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566301
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ci1', '96.g1', '144.e1', '144.u1', '144.x1', '144.z1', '144.bb1', '144.be1', '144.fx1'], 'contains': ['576.e1', '576.k1', '576.dv1', '576.cg1', '864.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 36933, 2676, 87091200], 'label': '6912.ia.288.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566302
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cj1', '96.g1', '144.bc1', '144.bf1', '144.fy1'], 'contains': ['576.f1', '576.l1', '576.dw1', '576.ch1', '864.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 36933, 93405314676, 87091200], 'label': '6912.ia.288.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '288.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566303
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1', '96.h1', '144.ft1', '144.u1', '144.bk1', '144.bl1', '144.bm1', '144.bn1', '144.bo1'], 'contains': ['576.e1', '576.n1', '576.dx1', '576.ci1', '864.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87305662080, 36933, 2676, 40279680], 'label': '6912.ia.288.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566304
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.a1', '144.v1', '144.bp1', '144.bq1', '144.br1', '144.bs1', '144.bt1', '144.bu1', '144.bv1', '144.bx1', '144.bw1'], 'contains': ['576.d1', '576.o1', '576.dy1', '576.cj1', '864.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87305662080, 93405312000, 36933, 40279680], 'label': '6912.ia.288.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566305
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1', '144.l1', '144.w1', '144.bp1', '144.by1', '144.bz1', '144.ca1', '144.cb1', '144.cc1', '144.cd1', '144.ce1', '144.cf1', '144.cg1', '144.ch1', '144.ci1', '144.fz1'], 'contains': ['576.d1', '576.p1', '576.x1', '576.dz1', '576.ck1', '864.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 40279680], 'label': '6912.ia.288.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566306
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bg1', '6.bi1', '9.b1'], 'contains': ['36.hp1', '36.hx1', '36.hy1', '36.ij1', '36.il1', '36.jp1', '36.jq1', '54.bc1', '72.pm1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.ce1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ce1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566307
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ee1', '96.i1', '144.f1', '144.x1', '144.bk1', '144.cj1', '144.ck1', '144.cl1', '144.gc1'], 'contains': ['576.e1', '576.s1', '576.y1', '576.ea1', '576.cl1', '864.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40280426, 36933, 2676, 40279680], 'label': '6912.ia.288.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566308
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ef1', '96.j1', '144.e1', '144.bl1', '144.cj1', '144.cm1', '144.cn1', '144.co1', '144.gd1'], 'contains': ['576.e1', '576.t1', '576.eb1', '576.cm1', '864.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 36933, 2676, 87091200], 'label': '6912.ia.288.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566309
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1', '144.k1', '144.bq1', '144.by1', '144.cp1', '144.cq1', '144.cr1', '144.cs1', '144.cu1', '144.ct1', '144.cv1', '144.ge1'], 'contains': ['576.d1', '576.u1', '576.ec1', '576.cn1', '864.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87091200], 'label': '6912.ia.288.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566310
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1', '144.m1', '144.y1', '144.br1', '144.ch1', '144.cp1', '144.cw1', '144.cx1', '144.cy1', '144.cz1', '144.da1', '144.db1', '144.dc1', '144.dd1', '144.de1', '144.fz1'], 'contains': ['576.d1', '576.x1', '576.ed1', '576.co1', '864.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87096887, 40279680], 'label': '6912.ia.288.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566311
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fj1', '96.k1', '144.g1', '144.z1', '144.bm1', '144.cm1', '144.df1', '144.dg1', '144.gc1'], 'contains': ['576.e1', '576.y1', '576.ee1', '576.cp1', '864.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [36933, 40310618, 87096887, 40279680], 'label': '6912.ia.288.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566312
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1', '144.l1', '144.ba1', '144.br1', '144.bz1', '144.cq1', '144.cw1', '144.dh1', '144.di1', '144.dj1', '144.dk1', '144.dl1', '144.dm1', '144.dq1', '144.dr1', '144.gi1'], 'contains': ['576.d1', '576.ba1', '576.bh1', '576.ef1', '576.cq1', '864.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87218571626, 36933, 40279680], 'label': '6912.ia.288.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566313
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fw1', '96.l1', '144.f1', '144.bb1', '144.bm1', '144.cn1', '144.dn1', '144.do1', '144.gj1'], 'contains': ['576.e1', '576.bb1', '576.bi1', '576.eg1', '576.cr1', '864.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218571626, 36933, 2676, 40279680], 'label': '6912.ia.288.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566314
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fx1', '96.l1', '144.bc1', '144.dp1', '144.gk1'], 'contains': ['576.f1', '576.bc1', '576.bj1', '576.eh1', '576.cs1', '864.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218571626, 36933, 93405314676, 40279680], 'label': '6912.ia.288.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566315
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.m1', '144.n1', '144.w1', '144.bs1', '144.ca1', '144.cq1', '144.cx1', '144.cy1', '144.dh1', '144.ds1', '144.dt1', '144.du1', '144.dv1', '144.dw1', '144.dx1', '144.gl1'], 'contains': ['576.d1', '576.bd1', '576.ei1', '576.ct1', '864.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.288.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566316
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gh1', '96.m1', '144.h1', '144.x1', '144.bn1', '144.cn1', '144.df1', '144.dy1', '144.gm1'], 'contains': ['576.e1', '576.be1', '576.ej1', '576.cu1', '864.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [30938, 36933, 87091200, 83468087], 'label': '6912.ia.288.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566317
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bg1', '6.bj1'], 'contains': ['36.hq1', '36.hz1', '36.ia1', '36.im1', '36.in1', '36.js1', '36.jt1', '54.bc1', '72.pn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 87222200426, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.18.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '18.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cf1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566318
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1', '144.m1', '144.bd1', '144.bp1', '144.cb1', '144.cr1', '144.cz1', '144.dq1', '144.ds1', '144.dt1', '144.dz1', '144.ea1', '144.ed1', '144.ee1', '144.ef1', '144.gi1'], 'contains': ['576.d1', '576.bh1', '576.ek1', '576.cv1', '864.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87265388087, 40279680], 'label': '6912.ia.288.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566319
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gr1', '96.n1', '144.g1', '144.be1', '144.bk1', '144.co1', '144.dy1', '144.eb1', '144.gj1'], 'contains': ['576.e1', '576.bi1', '576.el1', '576.cw1', '864.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36933, 40310618, 87265388087, 40279680], 'label': '6912.ia.288.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566320
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gs1', '96.n1', '144.bf1', '144.ec1', '144.gk1'], 'contains': ['576.f1', '576.bj1', '576.em1', '576.cx1', '864.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93445622618, 36933, 87265388087, 40279680], 'label': '6912.ia.288.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566321
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1', '144.n1', '144.ba1', '144.bt1', '144.by1', '144.cc1', '144.da1', '144.db1', '144.di1', '144.du1', '144.dz1', '144.ea1', '144.eg1', '144.eh1', '144.ei1', '144.gp1'], 'contains': ['576.d1', '576.bk1', '576.en1', '576.cy1', '864.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87261759287, 87091200], 'label': '6912.ia.288.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566322
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hb1', '96.o1', '144.h1', '144.bb1', '144.bo1', '144.cj1', '144.dg1', '144.eb1', '144.gq1'], 'contains': ['576.e1', '576.bl1', '576.eo1', '576.cz1', '864.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [30938, 36933, 87261759287, 87091200], 'label': '6912.ia.288.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566323
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hc1', '96.o1', '144.bc1', '144.ec1', '144.gs1'], 'contains': ['576.f1', '576.bn1', '576.ep1', '576.da1', '864.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405342938, 36933, 87261759287, 87091200], 'label': '6912.ia.288.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566324
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.bg1', '144.bu1', '144.ci1', '144.cs1', '144.de1', '144.dr1', '144.dx1', '144.ef1', '144.ei1', '144.ej1', '144.ek1', '144.el1', '144.en1', '144.em1', '144.eo1', '144.ep1', '144.eq1', '144.er1', '144.es1', '144.et1', '144.eu1', '144.ev1', '144.ew1', '144.ex1', '144.ey1', '144.ez1', '144.fa1', '144.fb1', '144.fc1', '144.gw1'], 'contains': ['576.d1', '576.br1', '576.bs1', '864.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 32929, 36933], 'label': '6912.ia.288.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566325
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1', '144.p1', '144.bq1', '144.cd1', '144.cx1', '144.dj1', '144.dz1', '144.ej1', '144.fe1', '144.fd1', '144.ff1', '144.fw1'], 'contains': ['576.d1', '576.eq1', '864.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 43908480, 36933, 87091200], 'label': '6912.ia.288.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566326
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.bi1', '144.bv1', '144.bz1', '144.cu1', '144.cz1', '144.du1', '144.ek1', '144.fe1', '144.fk1', '144.fg1', '144.fm1', '144.fl1', '144.fn1', '144.gx1'], 'contains': ['576.d1', '576.bt1', '576.bv1', '864.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218603809, 93405312000, 36933, 40279680], 'label': '6912.ia.288.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566327
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.eg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1', '144.p1', '144.v1', '144.ce1', '144.da1', '144.dk1', '144.ds1', '144.el1', '144.fk1', '144.fh1', '144.fo1', '144.ge1'], 'contains': ['576.d1', '576.er1', '864.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 87222199680, 36933, 87091200], 'label': '6912.ia.288.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566328
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bh1', '6.bi1', '6.bj1', '9.a1'], 'contains': ['36.c1', '36.ef1', '36.eh1', '36.ei1', '36.fg1', '36.ib1', '36.jm1', '54.bc1', '72.kd1'], 'core': '36.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.cg1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566329
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.lc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '144.bh1', '144.bv1', '144.ch1', '144.ct1', '144.dq1', '144.dv1', '144.eg1', '144.fb1', '144.fd1', '144.fg1', '144.fh1', '144.fi1', '144.fj1', '144.gw1'], 'contains': ['576.d1', '576.bs1', '864.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 93405312000, 36933, 87100665], 'label': '6912.ia.288.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566330
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '144.bh1', '144.bx1', '144.cf1', '144.cv1', '144.cy1', '144.dl1', '144.ea1', '144.ej1', '144.en1', '144.fk1', '144.fm1', '144.fi1', '144.fq1', '144.gy1'], 'contains': ['576.d1', '576.db1', '864.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 93405312000, 36933, 87091200], 'label': '6912.ia.288.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566331
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1', '144.bg1', '144.bw1', '144.ca1', '144.cu1', '144.dc1', '144.di1', '144.ed1', '144.em1', '144.fd1', '144.fl1', '144.fo1', '144.fi1', '144.fp1', '144.gy1'], 'contains': ['576.d1', '576.bu1', '864.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7653409, 93405312000, 36933, 87091200], 'label': '6912.ia.288.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566332
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '144.bj1', '144.bu1', '144.cb1', '144.cv1', '144.cw1', '144.dw1', '144.eh1', '144.eo1', '144.ff1', '144.fg1', '144.fo1', '144.fq1', '144.fp1', '144.gx1'], 'contains': ['576.d1', '576.bv1', '864.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 36933, 87265415329, 40279680], 'label': '6912.ia.288.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566333
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1', '144.t1', '144.y1', '144.bt1', '144.cd1', '144.cf1', '144.cr1', '144.dc1', '144.dk1', '144.dm1', '144.dv1', '144.ee1', '144.eh1', '144.ep1', '144.fn1', '144.gl1'], 'contains': ['576.d1', '576.es1', '864.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.288.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566334
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1', '144.bi1', '144.bx1', '144.cc1', '144.cs1', '144.dd1', '144.dh1', '144.ee1', '144.eq1', '144.ff1', '144.fl1', '144.fh1', '144.fj1', '144.fq1', '144.gz1'], 'contains': ['576.d1', '576.bw1', '864.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185944609, 93405312000, 36933, 87091200], 'label': '6912.ia.288.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566335
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '144.bj1', '144.bw1', '144.cg1', '144.ct1', '144.db1', '144.dm1', '144.dt1', '144.el1', '144.er1', '144.fe1', '144.fm1', '144.fj1', '144.fp1', '144.gz1'], 'contains': ['576.d1', '576.dc1', '864.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87222232609, 93405312000, 36933, 87091200], 'label': '6912.ia.288.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566336
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1', '144.t1', '144.bd1', '144.bs1', '144.ce1', '144.cg1', '144.cp1', '144.dd1', '144.dj1', '144.dl1', '144.dw1', '144.ed1', '144.eg1', '144.es1', '144.fn1', '144.gp1'], 'contains': ['576.d1', '576.et1', '864.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.288.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566337
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.il1', '96.p1', '144.i1', '144.bl1', '144.ck1', '144.df1', '144.dn1', '144.eb1', '144.fx1'], 'contains': ['576.e1', '576.eu1', '864.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43908480, 36933, 2676, 87091200], 'label': '6912.ia.288.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566338
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.im1', '96.q1', '144.i1', '144.u1', '144.cl1', '144.dg1', '144.do1', '144.dy1', '144.gd1'], 'contains': ['576.e1', '576.ev1', '864.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87222199680, 36933, 2676, 87091200], 'label': '6912.ia.288.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566339
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.i1', '12.bm1', '12.dl1', '18.bf1', '18.bh1', '18.bi1', '24.bd1', '24.dc1'], 'core': '12.i1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 43909226, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.n1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243566340
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bk1', '6.bl1', '9.a1'], 'contains': ['36.ej1', '36.ek1', '36.fq1', '36.fw1', '36.ib1', '36.iw1', '36.jc1', '54.be1', '72.ke1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.18.ch1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ch1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566341
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.in1', '96.r1', '144.j1', '144.z1', '144.bo1', '144.ck1', '144.co1', '144.do1', '144.gm1'], 'contains': ['576.e1', '576.ew1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 36933, 2676, 87091200], 'label': '6912.ia.288.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566342
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.io1', '96.s1', '144.j1', '144.be1', '144.bn1', '144.cl1', '144.cm1', '144.dn1', '144.gq1'], 'contains': ['576.e1', '576.ex1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87222200426, 36933, 2676, 87091200], 'label': '6912.ia.288.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566344
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.iq1', '96.s1', '144.bf1', '144.dp1', '144.gs1'], 'contains': ['576.f1', '576.ez1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87222200426, 36933, 93405314676, 87091200], 'label': '6912.ia.288.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566345
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '96.t1', '96.v1', '96.w1', '144.ft1', '144.fx1', '144.gc1', '144.gd1', '144.gj1', '144.gm1', '144.gq1'], 'contains': ['576.e1', '576.de1', '576.fa1', '864.a1'], 'core': '864.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 36933, 2676, 40279680], 'label': '6912.ia.288.bw1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '288.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566346
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lp1', '96.t1', '96.x1', '96.y1', '144.fy1', '144.gk1', '144.gs1'], 'contains': ['576.f1', '576.df1', '576.fb1', '864.a1'], 'core': '864.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 36933, 93405314676, 40279680], 'label': '6912.ia.288.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '288.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566347
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.w1', '96.y1', '144.gb1', '144.gg1', '144.gt1', '144.he1', '144.hf1'], 'contains': ['576.fc1', '864.a1', '1152.f1'], 'core': '864.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 93452849280, 36933, 40279680], 'label': '6912.ia.288.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '288.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.by1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566348
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lu1', '96.u1', '96.v1', '96.y1', '144.fv1', '144.go1', '144.gu1'], 'contains': ['576.fd1', '864.a1', '1152.g1'], 'core': '864.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 127370880, 36933, 40279680], 'label': '6912.ia.288.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '288.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566349
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lv1', '96.u1', '96.w1', '96.x1', '96.y1', '144.gv1'], 'contains': ['576.fe1', '864.a1', '1152.h1'], 'core': '864.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [127370880, 93525428474, 36933, 40279680], 'label': '6912.ia.288.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '288.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ca1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566350
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nd1', '96.bm1', '144.e1', '144.io1', '144.ip1'], 'contains': ['576.k1', '576.n1', '576.t1', '576.ff1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 36933, 2676, 87265382400], 'label': '6912.ia.288.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566351
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bm1', '9.b1'], 'contains': ['36.ic1', '36.ii1', '36.ij1', '36.io1', '36.ip1', '36.jd1', '36.je1', '54.bd1', '72.pw1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 47537280, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.18.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ci1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566352
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bm1', '144.k1', '144.iq1', '144.ir1', '144.is1', '144.it1'], 'contains': ['576.j1', '576.o1', '576.u1', '576.fg1', '864.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87265382400], 'label': '6912.ia.288.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '288.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566353
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1', '96.br1', '144.hu1', '144.w1', '144.iq1', '144.iu1', '144.iv1', '144.iw1', '144.ix1'], 'contains': ['576.j1', '576.p1', '576.bd1', '576.fh1', '864.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933], 'label': '6912.ia.288.cu1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566354
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.np1', '96.bn1', '96.bs1', '144.hg1', '144.x1', '144.io1'], 'contains': ['576.k1', '576.s1', '576.be1', '576.fi1', '864.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 2676], 'label': '6912.ia.288.cv1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '288.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566355
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bo1', '144.hv1', '144.w1', '144.ir1', '144.iu1', '144.iy1', '144.iz1', '144.ja1'], 'contains': ['576.j1', '576.x1', '576.bd1', '576.fj1', '864.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 83468087], 'label': '6912.ia.288.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566356
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nu1', '96.bo1', '144.hh1', '144.x1', '144.ip1'], 'contains': ['576.k1', '576.y1', '576.be1', '576.fk1', '864.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 6851, 36933, 83468087], 'label': '6912.ia.288.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '288.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566357
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bp1', '96.bt1', '144.hu1', '144.ba1', '144.ir1', '144.iv1', '144.iy1', '144.jb1', '144.jc1'], 'contains': ['576.j1', '576.ba1', '576.bk1', '576.fl1', '864.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87185912426], 'label': '6912.ia.288.cy1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566358
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.nz1', '96.bp1', '96.bu1', '144.hg1', '144.bb1', '144.ip1'], 'contains': ['576.k1', '576.bb1', '576.bl1', '576.fm1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 36933, 87185912426, 2676], 'label': '6912.ia.288.cz1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566359
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oa1', '96.bp1', '96.bv1', '144.bc1'], 'contains': ['576.l1', '576.bc1', '576.bn1', '576.fn1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 36933, 87185912426, 93405314676], 'label': '6912.ia.288.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '288.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.da1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566360
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bq1', '144.hv1', '144.ba1', '144.iq1', '144.iw1', '144.iz1', '144.jb1', '144.jd1'], 'contains': ['576.j1', '576.bh1', '576.bk1', '576.fo1', '864.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87261759287], 'label': '6912.ia.288.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.db1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566361
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.of1', '96.bq1', '144.hh1', '144.bb1', '144.io1'], 'contains': ['576.k1', '576.bi1', '576.bl1', '576.fp1', '864.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 6851, 36933, 87261759287], 'label': '6912.ia.288.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566362
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bk1', '6.bn1', '9.b1'], 'contains': ['36.ic1', '36.ik1', '36.il1', '36.iq1', '36.ir1', '36.jf1', '36.jg1', '54.be1', '72.px1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.18.cj1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cj1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243566363
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.og1', '96.bq1', '144.bc1'], 'contains': ['576.l1', '576.bj1', '576.bn1', '576.fq1', '864.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 93405318851, 36933, 87261759287], 'label': '6912.ia.288.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '288.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566364
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bw1', '144.hw1', '144.bg1', '144.is1', '144.ix1', '144.ja1', '144.jc1', '144.jd1', '144.jf1', '144.je1', '144.jg1', '144.jh1', '144.ji1', '144.jj1', '144.jk1', '144.jl1'], 'contains': ['576.j1', '576.br1', '576.bu1', '864.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933], 'label': '6912.ia.288.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.de1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566365
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bx1', '144.hw1', '144.bi1', '144.it1', '144.iv1', '144.iz1', '144.jf1', '144.jm1'], 'contains': ['576.j1', '576.bt1', '576.bw1', '864.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178324129, 36933], 'label': '6912.ia.288.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566366
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hx1', '144.bg1', '144.it1', '144.iu1', '144.jb1', '144.je1', '144.jm1'], 'contains': ['576.j1', '576.bs1', '576.bu1', '864.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87100665], 'label': '6912.ia.288.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.df1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566367
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hx1', '144.bi1', '144.is1', '144.iw1', '144.iy1', '144.jg1', '144.jm1'], 'contains': ['576.j1', '576.bv1', '576.bw1', '864.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87265415329], 'label': '6912.ia.288.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566368
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jm1', '96.br1', '96.bs1', '144.hi1', '144.jp1', '144.jq1'], 'contains': ['576.m1', '576.q1', '576.bf1', '576.fr1', '864.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 47537280, 7621226, 36933], 'label': '6912.ia.288.di1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '288.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566369
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jn1', '96.bt1', '96.bu1', '96.bv1', '144.hi1', '144.jp1', '144.jr1'], 'contains': ['576.m1', '576.z1', '576.bm1', '576.fs1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 47537280, 36933, 87185912426], 'label': '6912.ia.288.dj1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566370
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jo1', '96.bw1', '144.hj1', '144.jq1', '144.jr1', '144.js1', '144.jt1', '144.ju1', '144.jv1'], 'contains': ['576.m1', '576.bx1', '576.bz1', '864.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 32929, 47537280, 36933], 'label': '6912.ia.288.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566371
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jp1', '96.bx1', '144.hj1', '144.jp1', '144.js1'], 'contains': ['576.m1', '576.by1', '576.ca1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87178324129, 47537280, 36933], 'label': '6912.ia.288.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566372
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ol1', '96.by1', '144.f1', '144.bk1', '144.io1'], 'contains': ['576.n1', '576.s1', '576.bi1', '576.ft1', '864.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 36933, 746, 2676], 'label': '6912.ia.288.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566373
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bm1', '9.c1'], 'contains': ['36.ep1', '36.eq1', '36.et1', '36.eu1', '36.fk1', '36.fl1', '36.fs1', '36.ft1', '36.id1', '36.ie1', '36.if1', '36.is1', '36.it1', '36.iy1', '36.iz1', '54.bd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.18.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ck1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566374
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.om1', '96.bz1', '144.f1', '144.bm1', '144.ip1'], 'contains': ['576.n1', '576.y1', '576.bb1', '576.fu1', '864.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 40280426, 36933, 2676], 'label': '6912.ia.288.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566375
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.on1', '96.ca1', '144.g1', '144.bk1', '144.bm1'], 'contains': ['576.n1', '576.y1', '576.bi1', '576.fv1', '864.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218570880, 6851, 36933, 87096887], 'label': '6912.ia.288.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '288.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566376
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.oo1', '96.cb1', '144.h1', '144.io1', '144.ip1'], 'contains': ['576.n1', '576.be1', '576.bl1', '576.fw1', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6851, 36933, 83468087, 87265382400], 'label': '6912.ia.288.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566377
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.by1', '144.l1', '144.bp1', '144.iq1', '144.jx1', '144.jy1', '144.jz1', '144.ka1'], 'contains': ['576.o1', '576.p1', '576.bh1', '576.fx1', '864.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 746], 'label': '6912.ia.288.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566378
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bz1', '144.l1', '144.br1', '144.ir1', '144.jx1', '144.kb1', '144.kc1', '144.kd1'], 'contains': ['576.o1', '576.x1', '576.ba1', '576.fy1', '864.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880, 93405312000, 40280426, 36933], 'label': '6912.ia.288.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566379
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ca1', '144.m1', '144.bp1', '144.br1', '144.jy1', '144.kc1', '144.ke1', '144.kf1'], 'contains': ['576.o1', '576.x1', '576.bh1', '576.fz1', '864.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933, 87096887], 'label': '6912.ia.288.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gs1', 'old_label': '288.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ds1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566380
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cb1', '144.n1', '144.iq1', '144.ir1', '144.jz1', '144.kb1', '144.kg1', '144.kh1'], 'contains': ['576.o1', '576.bd1', '576.bk1', '576.ga1', '864.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 83468087, 87265382400], 'label': '6912.ia.288.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566381
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.bu1', '144.is1', '144.ka1', '144.kd1', '144.ke1', '144.kg1', '144.ki1', '144.kj1', '144.kk1', '144.kl1', '144.km1', '144.kn1', '144.ko1', '144.kp1'], 'contains': ['576.o1', '576.br1', '576.bv1', '864.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305662080, 93405312000, 32929, 36933], 'label': '6912.ia.288.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.du1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566382
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.bv1', '144.it1', '144.jx1', '144.kf1', '144.kh1', '144.ki1', '144.kq1', '144.kr1', '144.ks1'], 'contains': ['576.o1', '576.bt1', '576.bs1', '864.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 87178324129, 127403809, 36933], 'label': '6912.ia.288.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566383
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '144.bu1', '144.bv1', '144.jy1', '144.kc1', '144.kj1', '144.ks1'], 'contains': ['576.o1', '576.bs1', '576.bv1', '864.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218607813, 93405312000, 127403809, 36933], 'label': '6912.ia.288.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '288.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566384
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '18.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bl1', '6.bn1', '9.c1'], 'contains': ['36.er1', '36.es1', '36.ev1', '36.ew1', '36.fm1', '36.fo1', '36.fu1', '36.fv1', '36.id1', '36.ig1', '36.ih1', '36.iu1', '36.iv1', '36.ja1', '36.jb1', '54.be1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.18.cl1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243566385
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1', '144.is1', '144.it1', '144.jz1', '144.kb1', '144.kk1', '144.kq1'], 'contains': ['576.o1', '576.bu1', '576.bw1', '864.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83495329, 87265382400], 'label': '6912.ia.288.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566386
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cc1', '96.ch1', '144.hu1', '144.by1', '144.iq1', '144.kt1', '144.kv1', '144.kw1', '144.kx1'], 'contains': ['576.p1', '576.u1', '576.bk1', '576.gb1', '864.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87185912426], 'label': '6912.ia.288.dy1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566387
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jr1', '96.cc1', '96.ci1', '144.hi1', '144.ku1', '144.ky1'], 'contains': ['576.q1', '576.v1', '576.bm1', '576.gc1', '864.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 47537280, 36933, 87185912426], 'label': '6912.ia.288.dz1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566388
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.js1', '96.cc1', '96.cj1', '144.kz1'], 'contains': ['576.r1', '576.w1', '576.bo1', '576.gd1', '864.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 93452849280, 36933, 87185912426], 'label': '6912.ia.288.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.kz1', 'old_label': '288.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ea1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566389
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hy1', '144.ch1', '144.ci1', '144.iu1', '144.jx1', '144.jy1', '144.kt1'], 'contains': ['576.p1', '576.x1', '576.bs1', '864.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36239, 93405312000, 36933, 87100665], 'label': '6912.ia.288.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566390
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jt1', '96.cd1', '144.hl1', '144.jp1', '144.ku1'], 'contains': ['576.q1', '576.z1', '576.by1', '864.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 36933, 746, 87178300665], 'label': '6912.ia.288.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ec1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566391
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cd1', '144.ia1', '144.bz1', '144.iv1', '144.jx1', '144.kv1'], 'contains': ['576.p1', '576.ba1', '576.bt1', '864.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 36933, 746, 87178300665], 'label': '6912.ia.288.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '288.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ed1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566392
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ce1', '144.hz1', '144.ca1', '144.iu1', '144.ix1', '144.jz1', '144.kv1', '144.kw1'], 'contains': ['576.p1', '576.bd1', '576.bu1', '864.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 7621226, 36933, 7629945], 'label': '6912.ia.288.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ee1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566393
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jw1', '96.ce1', '144.hk1', '144.jq1', '144.ku1'], 'contains': ['576.q1', '576.bf1', '576.bz1', '864.bz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [47537280, 7621226, 36933, 7629945], 'label': '6912.ia.288.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '288.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566394
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hy1', '144.bz1', '144.cb1', '144.iw1', '144.jy1', '144.ka1', '144.kw1'], 'contains': ['576.p1', '576.bh1', '576.bv1', '864.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 746, 87218580345], 'label': '6912.ia.288.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566395
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.bo1', '12.bp1'], 'contains': ['48.a1', '48.b1', '48.c1', '48.g1', '72.is1', '72.ja1', '96.bd1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.a1', '48.b1', '48.c1', '48.g1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566396
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cf1', '144.hz1', '144.cc1', '144.iv1', '144.iw1', '144.jz1', '144.kt1', '144.kx1'], 'contains': ['576.p1', '576.bk1', '576.bw1', '864.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87185912426, 87185921145], 'label': '6912.ia.288.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566397
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jy1', '96.cf1', '144.hk1', '144.jp1', '144.ky1'], 'contains': ['576.q1', '576.bm1', '576.ca1', '864.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 36933, 87185912426, 87185921145], 'label': '6912.ia.288.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ei1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566398
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.jz1', '96.cf1', '144.kz1'], 'contains': ['576.r1', '576.bo1', '576.cc1', '864.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93452849280, 36933, 87185912426, 87185921145], 'label': '6912.ia.288.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.kz1', 'old_label': '288.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ej1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566399
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cg1', '144.ia1', '144.ci1', '144.ix1', '144.ka1', '144.kx1', '144.lb1', '144.la1', '144.lc1', '144.ld1', '144.le1', '144.lf1'], 'contains': ['576.p1', '576.br1', '864.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 746], 'label': '6912.ia.288.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ek1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566400
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kb1', '96.cg1', '144.hl1', '144.jq1', '144.ky1', '144.lg1', '144.lh1', '144.li1', '144.lj1'], 'contains': ['576.q1', '576.bx1', '864.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 47537280, 36933, 746], 'label': '6912.ia.288.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.el1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566401
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kc1', '96.cg1', '144.kz1', '144.lk1', '144.ll1'], 'contains': ['576.r1', '576.cb1', '864.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9465, 93452849280, 36933, 746], 'label': '6912.ia.288.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '288.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.em1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566402
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.po1', '96.ch1', '96.ci1', '96.cj1', '144.hg1', '144.cj1', '144.io1'], 'contains': ['576.s1', '576.t1', '576.bl1', '576.ge1', '864.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 2676], 'label': '6912.ia.288.en1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.en1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566403
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pp1', '96.ck1', '144.hh1', '144.cj1', '144.ip1'], 'contains': ['576.t1', '576.y1', '576.bl1', '576.gf1', '864.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6851, 87185911680, 36933, 87261759287], 'label': '6912.ia.288.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566404
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pq1', '96.cl1', '96.cm1', '144.hg1', '144.cn1', '144.ip1'], 'contains': ['576.t1', '576.bb1', '576.be1', '576.gg1', '864.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 7621226, 36933, 2676], 'label': '6912.ia.288.ep1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ep1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566405
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.pr1', '96.cn1', '144.hh1', '144.cn1', '144.io1'], 'contains': ['576.t1', '576.be1', '576.bi1', '576.gh1', '864.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6851, 87185911680, 36933, 83468087], 'label': '6912.ia.288.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566406
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': ['288.mo1', '288.ms1', '288.mu1', '288.mp1', '288.mv1', '288.mw1', '288.f1', '288.mg1', '288.mh1'], 'conjugacy_class_count': 1, 'contained_in': ['8.j1', '12.k1', '12.dq1'], 'contains': ['48.d1', '48.e1', '48.f1', '72.mc1', '72.ms1', '96.bf1'], 'core': '24.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 36933, 746, 2676], 'label': '6912.ia.24.e1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.e1', 'normal_contained_in': ['6.b1'], 'normal_contains': ['48.d1', '48.e1', '48.f1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566407
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ck1', '144.hv1', '144.by1', '144.ir1', '144.kt1', '144.ln1', '144.lo1', '144.lp1'], 'contains': ['576.u1', '576.x1', '576.bk1', '576.gi1', '864.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87261759287], 'label': '6912.ia.288.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.er1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566408
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kf1', '96.cl1', '96.co1', '144.hi1', '144.ku1', '144.lq1'], 'contains': ['576.v1', '576.z1', '576.bf1', '576.gj1', '864.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 47537280, 7621226, 36933], 'label': '6912.ia.288.es1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.es1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566409
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cm1', '96.co1', '144.hu1', '144.cq1', '144.ir1', '144.kv1', '144.ln1', '144.lr1', '144.ls1'], 'contains': ['576.u1', '576.ba1', '576.bd1', '576.gk1', '864.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 93405312000, 7621226, 36933], 'label': '6912.ia.288.et1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.et1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566410
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cn1', '144.hv1', '144.cq1', '144.iq1', '144.kw1', '144.lo1', '144.lr1', '144.lt1'], 'contains': ['576.u1', '576.bd1', '576.bh1', '576.gl1', '864.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 83468087], 'label': '6912.ia.288.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566411
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cp1', '144.hw1', '144.cs1', '144.is1', '144.kx1', '144.lp1', '144.ls1', '144.lt1', '144.lv1', '144.lu1', '144.lw1', '144.lx1', '144.ly1', '144.lz1', '144.ma1', '144.mb1'], 'contains': ['576.u1', '576.br1', '576.bw1', '864.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 32929, 36933], 'label': '6912.ia.288.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ev1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566412
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cq1', '144.hw1', '144.cu1', '144.it1', '144.kv1', '144.lo1', '144.lv1', '144.mc1'], 'contains': ['576.u1', '576.bt1', '576.bu1', '864.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178324129, 36933, 83495329], 'label': '6912.ia.288.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ex1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566413
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hx1', '144.cs1', '144.it1', '144.kt1', '144.lr1', '144.lu1', '144.mc1'], 'contains': ['576.u1', '576.bs1', '576.bw1', '864.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933, 87100665], 'label': '6912.ia.288.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ew1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566414
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hx1', '144.cu1', '144.is1', '144.kw1', '144.ln1', '144.lw1', '144.mc1'], 'contains': ['576.u1', '576.bu1', '576.bv1', '864.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83495329, 87265415329], 'label': '6912.ia.288.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ey1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566415
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kj1', '96.cp1', '144.hj1', '144.ky1', '144.lq1', '144.md1', '144.me1', '144.mf1', '144.mg1'], 'contains': ['576.v1', '576.bx1', '576.ca1', '864.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185911680, 32929, 47537280, 36933], 'label': '6912.ia.288.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ez1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566416
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kk1', '96.cq1', '144.hj1', '144.ku1', '144.md1'], 'contains': ['576.v1', '576.by1', '576.bz1', '864.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178324129, 79833600, 36933, 83495329], 'label': '6912.ia.288.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fa1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566417
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': ['288.js1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.e1', '12.h1', '12.bx1', '12.cm1', '12.cz1', '12.df1'], 'contains': ['48.bj1', '72.a1', '72.b1', '72.lp1', '96.t1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.24.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.a1', '12.e1', '12.h1'], 'normal_contains': ['72.a1', '72.b1', '96.b1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '3456.jo', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566418
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kl1', '96.cp1', '144.kz1', '144.mh1', '144.mi1'], 'contains': ['576.w1', '576.cb1', '576.cc1', '864.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 32929, 93452849280, 36933], 'label': '6912.ia.288.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '288.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566419
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hy1', '144.bz1', '144.cw1', '144.iy1', '144.kc1', '144.kd1', '144.ln1'], 'contains': ['576.x1', '576.ba1', '576.bv1', '864.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87218580345], 'label': '6912.ia.288.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566420
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ib1', '144.ca1', '144.iu1', '144.ja1', '144.kb1', '144.ln1', '144.lo1'], 'contains': ['576.x1', '576.bd1', '576.bu1', '864.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 7629945, 83468087], 'label': '6912.ia.288.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566421
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ic1', '144.bz1', '144.cz1', '144.iz1', '144.jx1', '144.kf1', '144.lo1'], 'contains': ['576.x1', '576.bh1', '576.bt1', '864.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87178300665], 'label': '6912.ia.288.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fe1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566422
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.id1', '144.cb1', '144.cw1', '144.cz1', '144.jy1', '144.kc1', '144.ke1'], 'contains': ['576.x1', '576.bh1', '576.bv1', '864.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87218580345, 87096887], 'label': '6912.ia.288.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gs1', 'old_label': '288.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ff1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566423
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ib1', '144.cc1', '144.iy1', '144.iz1', '144.kb1', '144.kt1', '144.lp1'], 'contains': ['576.x1', '576.bk1', '576.bw1', '864.co1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87261759287, 87185921145], 'label': '6912.ia.288.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566424
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ic1', '144.ci1', '144.de1', '144.ja1', '144.kd1', '144.ke1', '144.lp1', '144.ml1', '144.mj1', '144.mk1', '144.mm1', '144.mn1', '144.mo1', '144.mp1', '144.mq1'], 'contains': ['576.x1', '576.br1', '864.cp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 36933], 'label': '6912.ia.288.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fh1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566425
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.id1', '144.ch1', '144.de1', '144.kc1', '144.kf1', '144.mr1', '144.ms1'], 'contains': ['576.x1', '576.bs1', '864.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933, 87100665], 'label': '6912.ia.288.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bm1', 'old_label': '288.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fi1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566426
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.km1', '96.cr1', '144.hk1', '144.jp1', '144.lq1'], 'contains': ['576.z1', '576.bf1', '576.ca1', '864.cr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 7621226, 36933, 87185921145], 'label': '6912.ia.288.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566427
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kn1', '96.cs1', '144.hk1', '144.jr1', '144.ku1'], 'contains': ['576.z1', '576.bm1', '576.bz1', '864.ct1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 36933, 87185912426, 7629945], 'label': '6912.ia.288.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566428
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['288.jq1', '288.mx1', '288.my1', '288.jr1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.c1', '12.g1', '12.ck1', '12.cw1', '12.dd1', '12.dj1'], 'contains': ['48.cm1', '72.a1', '72.c1', '72.lt1', '96.de1'], 'core': '24.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.24.c1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1', 'normal_contained_in': ['8.a1', '12.b1', '12.c1', '12.g1'], 'normal_contains': ['72.a1', '72.c1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.d1', 'projective_image': '3456.jo', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243566429
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ko1', '96.ct1', '144.hl1', '144.jr1', '144.lq1', '144.mu1', '144.mv1', '144.mw1', '144.mx1'], 'contains': ['576.z1', '576.bx1', '864.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 47537280, 36933, 87178291946], 'label': '6912.ia.288.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fl1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566430
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cr1', '144.hz1', '144.dh1', '144.iv1', '144.iy1', '144.kb1', '144.lr1', '144.ls1'], 'contains': ['576.ba1', '576.bd1', '576.bw1', '864.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 7621226, 36933, 87185921145], 'label': '6912.ia.288.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566431
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hy1', '144.dq1', '144.dr1', '144.jb1', '144.jx1', '144.kc1', '144.lr1'], 'contains': ['576.ba1', '576.bh1', '576.bs1', '864.cs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87178327439, 93405312000, 36933, 87100665], 'label': '6912.ia.288.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '288.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566432
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cs1', '144.hz1', '144.di1', '144.jb1', '144.jc1', '144.kb1', '144.kv1', '144.ln1'], 'contains': ['576.ba1', '576.bk1', '576.bu1', '864.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87185912426, 7629945], 'label': '6912.ia.288.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566433
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ct1', '144.ia1', '144.dr1', '144.jc1', '144.kd1', '144.ls1', '144.mz1', '144.my1', '144.na1', '144.nb1', '144.nc1', '144.nd1'], 'contains': ['576.ba1', '576.br1', '864.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87178291946], 'label': '6912.ia.288.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566434
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ib1', '144.dh1', '144.iw1', '144.iz1', '144.jz1', '144.lr1', '144.lt1'], 'contains': ['576.bd1', '576.bh1', '576.bw1', '864.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87185921145, 83468087], 'label': '6912.ia.288.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566435
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cu1', '144.ie1', '144.du1', '144.iv1', '144.iz1', '144.kh1', '144.kv1', '144.lo1'], 'contains': ['576.bd1', '576.bk1', '576.bt1', '864.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 83468087, 87178300665], 'label': '6912.ia.288.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566436
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.if1', '144.du1', '144.iw1', '144.iy1', '144.kg1', '144.kw1', '144.ln1'], 'contains': ['576.bd1', '576.bk1', '576.bv1', '864.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87265391865, 36933, 83468087], 'label': '6912.ia.288.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566437
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cv1', '144.ie1', '144.dx1', '144.ix1', '144.ja1', '144.kg1', '144.ls1', '144.lt1', '144.nh1', '144.ng1', '144.ni1', '144.nj1', '144.nk1', '144.nl1', '144.nm1', '144.nn1'], 'contains': ['576.bd1', '576.br1', '864.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 83498639], 'label': '6912.ia.288.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ft1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566438
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.if1', '144.dx1', '144.iu1', '144.kh1', '144.lr1', '144.no1', '144.np1'], 'contains': ['576.bd1', '576.bs1', '864.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7656719, 93405312000, 36933, 87100665], 'label': '6912.ia.288.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fu1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566439
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['288.jz1', '288.mz1', '288.na1', '288.ka1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.d1', '12.f1', '12.i1', '12.bm1', '12.cn1', '12.cx1', '12.dl1'], 'contains': ['72.b1', '72.c1', '72.lu1', '96.v1', '96.di1'], 'core': '24.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.24.d1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1', 'normal_contained_in': ['8.a1', '12.d1', '12.f1', '12.i1'], 'normal_contains': ['72.b1', '72.c1'], 'normalizer': '1.a1', 'old_label': '24.e1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243566440
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ku1', '96.cu1', '144.hm1', '144.jp1', '144.ku1'], 'contains': ['576.bf1', '576.bm1', '576.by1', '864.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [79833600, 36933, 83468087, 87178300665], 'label': '6912.ia.288.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '288.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566441
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kv1', '96.cv1', '144.hm1', '144.jq1', '144.lq1', '144.nr1', '144.ns1', '144.nt1', '144.nu1'], 'contains': ['576.bf1', '576.bx1', '864.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 79870533, 36933, 83498639], 'label': '6912.ia.288.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566442
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ib1', '144.di1', '144.jb1', '144.jd1', '144.jz1', '144.kw1', '144.lo1'], 'contains': ['576.bh1', '576.bk1', '576.bu1', '864.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87261759287, 7629945], 'label': '6912.ia.288.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '288.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566443
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ic1', '144.dr1', '144.ef1', '144.jd1', '144.ka1', '144.ke1', '144.lt1', '144.nz1', '144.nx1', '144.ny1', '144.oa1', '144.ob1', '144.oc1', '144.od1', '144.oe1'], 'contains': ['576.bh1', '576.br1', '864.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87218571626, 36933], 'label': '6912.ia.288.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fy1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566444
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.id1', '144.dq1', '144.ef1', '144.jy1', '144.kf1', '144.of1', '144.og1'], 'contains': ['576.bh1', '576.bs1', '864.dc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87218571626, 36933, 87100665], 'label': '6912.ia.288.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bm1', 'old_label': '288.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.fz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566445
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cw1', '144.ie1', '144.ei1', '144.jc1', '144.jd1', '144.kg1', '144.kx1', '144.lp1', '144.ok1', '144.oj1', '144.ol1', '144.om1', '144.on1', '144.oo1', '144.op1', '144.oq1'], 'contains': ['576.bk1', '576.br1', '864.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87261789839], 'label': '6912.ia.288.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ga1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566446
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.if1', '144.ei1', '144.jb1', '144.kh1', '144.kt1', '144.or1', '144.os1'], 'contains': ['576.bk1', '576.bs1', '864.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.288.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566447
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.kx1', '96.cw1', '144.hm1', '144.jr1', '144.ky1', '144.ou1', '144.ov1', '144.ow1', '144.ox1'], 'contains': ['576.bm1', '576.bx1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 79870533, 36933, 87261789839], 'label': '6912.ia.288.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566448
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ky1', '96.cw1', '144.kz1', '144.oz1', '144.pa1'], 'contains': ['576.bo1', '576.cb1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 93485182533, 36933, 87261789839], 'label': '6912.ia.288.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '288.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gd1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566449
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cx1', '144.c1', '144.ek1', '144.jf1', '144.ki1', '144.lb1', '144.lv1', '144.ml1', '144.mz1', '144.nh1', '144.nz1', '144.ok1'], 'contains': ['576.br1', '576.bt1', '864.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87178300665], 'label': '6912.ia.288.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566450
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.j1', '12.k1', '12.m1', '12.dq1', '12.dr1', '12.q1', '12.s1', '12.z1', '12.bd1', '12.dt1', '12.du1', '18.a1', '18.f1', '24.f1'], 'core': '24.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 2676, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.6.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566451
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '8.b1', '12.bl1'], 'contains': ['48.bk1', '48.bo1', '48.bv1', '48.fr1', '72.ir1', '72.is1', '96.z1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bb1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566452
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ig1', '144.fb1', '144.fc1', '144.je1', '144.ki1', '144.kj1', '144.la1', '144.lu1', '144.mj1', '144.mk1', '144.my1', '144.ng1', '144.nx1', '144.ny1', '144.oj1'], 'contains': ['576.br1', '576.bs1', '864.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 36933, 87100665, 87124129], 'label': '6912.ia.288.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ge1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566453
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cy1', '144.ih1', '144.em1', '144.je1', '144.jl1', '144.kk1', '144.lc1', '144.lv1', '144.lw1', '144.mm1', '144.na1', '144.ni1', '144.nj1', '144.oa1', '144.ol1', '144.om1'], 'contains': ['576.br1', '576.bu1', '864.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 83480268], 'label': '6912.ia.288.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566454
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ig1', '144.ek1', '144.eo1', '144.jg1', '144.kj1', '144.kp1', '144.ld1', '144.lw1', '144.mn1', '144.mo1', '144.nb1', '144.nk1', '144.ob1', '144.oc1', '144.on1'], 'contains': ['576.br1', '576.bv1', '864.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87305671545], 'label': '6912.ia.288.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566455
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cz1', '144.ih1', '144.eq1', '144.jf1', '144.jg1', '144.kk1', '144.le1', '144.lu1', '144.mb1', '144.mp1', '144.nc1', '144.nl1', '144.nm1', '144.od1', '144.oo1', '144.op1'], 'contains': ['576.br1', '576.bw1', '864.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 32929, 36933, 87261771468], 'label': '6912.ia.288.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gi1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566456
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.da1', '144.ii1', '144.et1', '144.jh1', '144.kl1', '144.lf1', '144.lx1', '144.mj1', '144.mz1', '144.ni1', '144.ob1', '144.oo1'], 'contains': ['576.br1', '864.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 34210, 36933], 'label': '6912.ia.288.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566457
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ij1', '144.et1', '144.eu1', '144.ji1', '144.km1', '144.kn1', '144.la1', '144.ly1', '144.mk1', '144.mq1', '144.nb1', '144.nj1', '144.nz1', '144.oc1', '144.op1'], 'contains': ['576.br1', '864.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40313890, 36933], 'label': '6912.ia.288.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566458
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.db1', '144.ii1', '144.ev1', '144.jj1', '144.km1', '144.lb1', '144.lz1', '144.mn1', '144.nd1', '144.nl1', '144.nx1', '144.ol1'], 'contains': ['576.br1', '864.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87178325410], 'label': '6912.ia.288.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '288.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566459
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dc1', '144.ik1', '144.ew1', '144.jh1', '144.ji1', '144.ko1', '144.lc1', '144.lz1', '144.ma1', '144.mm1', '144.nc1', '144.ng1', '144.nn1', '144.od1', '144.ok1', '144.on1'], 'contains': ['576.br1', '864.dn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 7654690, 36933], 'label': '6912.ia.288.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566460
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ij1', '144.ev1', '144.ey1', '144.jk1', '144.kl1', '144.kn1', '144.ld1', '144.ma1', '144.ml1', '144.mo1', '144.my1', '144.nm1', '144.ny1', '144.oe1', '144.om1'], 'contains': ['576.br1', '864.do1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87218605090], 'label': '6912.ia.288.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '288.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566461
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dd1', '144.ik1', '144.ez1', '144.jj1', '144.jk1', '144.ko1', '144.le1', '144.lx1', '144.ly1', '144.mp1', '144.na1', '144.nh1', '144.nk1', '144.oa1', '144.oj1', '144.oq1'], 'contains': ['576.br1', '864.dp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87185945890], 'label': '6912.ia.288.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '288.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.go1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566462
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '8.c1', '12.bl1'], 'contains': ['48.bk1', '48.bs1', '48.by1', '48.fs1', '72.it1', '72.iu1', '96.ba1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bc1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566463
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ig1', '144.ek1', '144.fg1', '144.jm1', '144.ki1', '144.ks1', '144.mc1'], 'contains': ['576.bt1', '576.bs1', '576.bv1', '864.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 127403809, 36933, 87305671545], 'label': '6912.ia.288.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '288.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566464
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.df1', '144.ih1', '144.fl1', '144.jf1', '144.jm1', '144.kq1', '144.lv1', '144.mc1'], 'contains': ['576.bt1', '576.bu1', '576.bw1', '864.dx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87178324129, 36933, 83480268], 'label': '6912.ia.288.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.p1', 'old_label': '288.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566465
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.il1', '144.em1', '144.je1', '144.kq1', '144.mc1', '144.mr1', '144.of1'], 'contains': ['576.bs1', '576.bu1', '864.dr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7653409, 93405312000, 36933, 87100665], 'label': '6912.ia.288.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '288.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566466
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.in1', '144.eo1', '144.fg1', '144.kj1', '144.ks1', '144.no1', '144.or1'], 'contains': ['576.bs1', '576.bv1', '864.ds1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87265391865, 127403809, 36933], 'label': '6912.ia.288.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bp1', 'old_label': '288.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566467
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.il1', '144.eq1', '144.jm1', '144.kq1', '144.lu1', '144.ms1', '144.og1'], 'contains': ['576.bs1', '576.bw1', '864.dt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185944609, 93405312000, 36933, 87100665], 'label': '6912.ia.288.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '288.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gs1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566468
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.im1', '144.ex1', '144.kr1', '144.mr1', '144.np1', '144.og1', '144.or1'], 'contains': ['576.bs1', '864.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43942690, 36933, 87100665], 'label': '6912.ia.288.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '288.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566469
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.im1', '144.fa1', '144.kr1', '144.ms1', '144.no1', '144.of1', '144.os1'], 'contains': ['576.bs1', '864.dv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87222233890, 87100665], 'label': '6912.ia.288.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '288.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566470
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dh1', '144.in1', '144.fb1', '144.ks1', '144.np1', '144.os1'], 'contains': ['576.bs1', '864.dw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127388748, 93405312000, 36933, 87124129], 'label': '6912.ia.288.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '288.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566471
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.il1', '144.fl1', '144.jg1', '144.jm1', '144.kk1', '144.lw1', '144.mc1'], 'contains': ['576.bu1', '576.bv1', '576.bw1', '864.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 83480268, 87265415329], 'label': '6912.ia.288.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.p1', 'old_label': '288.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566472
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lh1', '96.cx1', '144.hr1', '144.js1', '144.lg1', '144.md1', '144.mu1', '144.nr1', '144.ou1'], 'contains': ['576.bx1', '576.by1', '864.dg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [32929, 47537280, 36933, 87178300665], 'label': '6912.ia.288.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gy1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566473
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '8.d1', '12.bl1'], 'contains': ['48.bk1', '48.ce1', '48.ci1', '48.ft1', '72.iv1', '72.iw1', '72.ix1', '96.bb1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bd1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566474
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.li1', '96.cy1', '144.ho1', '144.jv1', '144.lh1', '144.md1', '144.mv1', '144.ns1', '144.ov1'], 'contains': ['576.bx1', '576.bz1', '864.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [32929, 79833600, 36933, 83480268], 'label': '6912.ia.288.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.gz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566475
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lj1', '96.cz1', '144.ho1', '144.js1', '144.li1', '144.mg1', '144.mw1', '144.nt1', '144.ow1'], 'contains': ['576.bx1', '576.ca1', '864.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [32929, 79833600, 36933, 87261771468], 'label': '6912.ia.288.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ha1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566476
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lk1', '96.da1', '144.hp1', '144.jt1', '144.lj1', '144.me1', '144.mu1', '144.ns1', '144.ow1'], 'contains': ['576.bx1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 47537280, 34210, 36933], 'label': '6912.ia.288.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566477
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.hp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ll1', '96.db1', '144.hp1', '144.ju1', '144.lg1', '144.mf1', '144.mx1', '144.nt1', '144.ov1'], 'contains': ['576.bx1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 47537280, 36933, 87178325410], 'label': '6912.ia.288.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566478
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lm1', '96.dc1', '144.hq1', '144.jt1', '144.lh1', '144.mf1', '144.mw1', '144.nu1', '144.ou1'], 'contains': ['576.bx1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 7654690, 47537280, 36933], 'label': '6912.ia.288.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '288.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566479
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ln1', '96.dd1', '144.hq1', '144.ju1', '144.li1', '144.me1', '144.mv1', '144.nr1', '144.ox1'], 'contains': ['576.bx1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 47537280, 36933, 87185945890], 'label': '6912.ia.288.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '288.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.he1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566480
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '96.de1', '96.di1', '96.dk1', '144.hr1', '144.jv1', '144.lj1', '144.mg1', '144.mx1', '144.nu1', '144.ox1'], 'contains': ['576.bx1', '864.b1'], 'core': '864.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [9465, 32929, 47537280, 36933], 'label': '6912.ia.288.hf1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '288.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hf1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566481
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lo1', '96.df1', '144.ho1', '144.js1', '144.md1'], 'contains': ['576.by1', '576.bz1', '576.ca1', '864.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178324129, 79833600, 36933, 83480268], 'label': '6912.ia.288.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lz1', 'old_label': '288.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566482
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.dk1', '96.dl1', '144.fs1', '144.jo1', '144.nf1', '144.oi1', '144.oy1'], 'contains': ['864.b1', '1152.e1'], 'core': '864.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [9465, 32929, 36933, 93405314676], 'label': '6912.ia.288.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '288.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566483
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lq1', '96.cz1', '144.lk1', '144.mi1', '144.oz1'], 'contains': ['576.cb1', '576.cc1', '864.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [32929, 93485145600, 36933, 87261771468], 'label': '6912.ia.288.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '288.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hi1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243566484
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '8.i1', '12.dp1'], 'contains': ['48.cr1', '48.dp1', '48.eb1', '72.lw1', '72.lz1', '96.z1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 120115956, 9465, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.24.da1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566485
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lr1', '96.da1', '144.ll1', '144.mh1', '144.oz1'], 'contains': ['576.cb1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9465, 34210, 93452849280, 36933], 'label': '6912.ia.288.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '288.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566486
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ls1', '96.dd1', '144.lk1', '144.mh1', '144.pa1'], 'contains': ['576.cb1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [9465, 93452849280, 36933, 87185945890], 'label': '6912.ia.288.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '288.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566487
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lt1', '96.de1', '96.dj1', '96.dl1', '144.ll1', '144.mi1', '144.pa1'], 'contains': ['576.cb1', '864.b1'], 'core': '864.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [9465, 32929, 93452849280, 36933], 'label': '6912.ia.288.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '288.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566488
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lu1', '96.dg1', '96.di1', '96.dl1', '144.hs1', '144.nv1', '144.pb1'], 'contains': ['864.b1', '1152.g1'], 'core': '864.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 9465, 32929, 36933], 'label': '6912.ia.288.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '288.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566489
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lu1', '96.dh1', '144.ht1', '144.nw1', '144.pc1'], 'contains': ['864.dw1', '1152.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127388748, 36933, 87124129], 'label': '6912.ia.288.hn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '288.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566490
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lv1', '96.dg1', '96.dj1', '96.dk1', '96.dl1', '144.pd1'], 'contains': ['864.b1', '1152.h1'], 'core': '864.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [9465, 93525428474, 32929, 36933], 'label': '6912.ia.288.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1', 'old_label': '288.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ho1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566491
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.lv1', '96.dh1', '144.pe1'], 'contains': ['864.dw1', '1152.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127388748, 93525428474, 36933, 87124129], 'label': '6912.ia.288.hp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.fe1', 'old_label': '288.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566492
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dw1', '144.ft1', '144.pi1', '144.pj1', '144.pk1'], 'contains': ['576.dg1', '576.cd1', '576.de1', '576.dx1', '576.ci1', '864.eo1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 127370880, 87178291200, 2676], 'label': '6912.ia.288.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566493
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ef1', '144.e1', '144.pi1', '144.px1', '144.py1', '144.qb1'], 'contains': ['576.dg1', '576.dh1', '576.dv1', '576.eb1', '576.ff1', '864.ev1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 87178291200, 2676, 87091200], 'label': '6912.ia.288.jh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566494
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eg1', '144.f1', '144.pj1', '144.px1', '144.pz1', '144.qe1'], 'contains': ['576.dg1', '576.dk1', '576.dl1', '576.ea1', '576.eg1', '576.ft1', '576.fu1', '864.ew1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40280426, 87178328133, 2676, 40279680], 'label': '6912.ia.288.ji1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ji1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566495
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '8.j1', '12.dp1'], 'contains': ['48.cr1', '48.dy1', '48.en1', '72.mb1', '72.mc1', '96.ba1'], 'core': '144.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 32929, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.24.db1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566496
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eh1', '144.g1', '144.pj1', '144.py1', '144.qa1', '144.qe1'], 'contains': ['576.dg1', '576.dl1', '576.ee1', '576.el1', '576.fv1', '864.ex1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40304216, 87178291200, 87096887, 40279680], 'label': '6912.ia.288.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ht1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566497
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ei1', '144.h1', '144.pk1', '144.px1', '144.qa1', '144.qf1'], 'contains': ['576.dg1', '576.dm1', '576.ej1', '576.eo1', '576.fw1', '864.ey1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.288.jk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566498
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ej1', '144.i1', '144.pi1', '144.pz1', '144.qa1', '144.qb1'], 'contains': ['576.dg1', '576.eu1', '576.ev1', '864.ez1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [43908480, 87178328133, 2676, 87091200], 'label': '6912.ia.288.jl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566499
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ek1', '144.j1', '144.pk1', '144.py1', '144.pz1', '144.qf1'], 'contains': ['576.dg1', '576.ew1', '576.ex1', '864.fa1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [43909226, 87178328133, 2676, 87091200], 'label': '6912.ia.288.jm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.hw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566500
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ed1', '96.el1', '144.ft1', '144.qb1', '144.qe1', '144.qf1'], 'contains': ['576.dg1', '576.dx1', '576.fa1', '864.fb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 87178328133, 2676, 40279680], 'label': '6912.ia.288.jn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '288.hx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566501
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.ed1', '144.fu1', '144.qc1', '144.qd1', '144.qg1'], 'contains': ['576.c1', '864.fb1', '1152.m1'], 'core': '576.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 47537280, 87178328133, 40279680], 'label': '6912.ia.288.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.hy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566502
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ed1', '96.em1', '144.fv1', '144.qh1'], 'contains': ['576.fd1', '864.fb1', '1152.n1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120116474, 127370880, 87178328133, 40279680], 'label': '6912.ia.288.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bd1', 'old_label': '288.hz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566503
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dm1', '144.e1', '144.pf1'], 'contains': ['576.cd1', '576.dh1', '576.cg1', '576.cm1', '576.ff1', '864.dz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87178291200, 7657413, 87128133, 2676], 'label': '6912.ia.288.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.ia1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566504
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.dn1', '144.f1', '144.pj1', '144.pf1'], 'contains': ['576.cd1', '576.dk1', '576.dl1', '576.cl1', '576.cr1', '576.ft1', '576.fu1', '864.ea1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 40280426, 87178291200, 2676], 'label': '6912.ia.288.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ib1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566505
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.do1', '144.g1', '144.pj1'], 'contains': ['576.cd1', '576.dl1', '576.cp1', '576.cw1', '576.fv1', '864.eb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87105687, 87178328133, 40310618], 'label': '6912.ia.288.hs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '288.ic1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566506
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '8.k1', '12.dp1'], 'contains': ['48.cr1', '48.ew1', '48.ff1', '72.me1', '72.mg1', '72.mh1', '96.bb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 32929, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.24.dc1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566507
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dp1', '144.h1', '144.pf1'], 'contains': ['576.cd1', '576.dm1', '576.cu1', '576.cz1', '576.fw1', '864.ec1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87178291200, 24536, 87128133, 83476887], 'label': '6912.ia.288.ht1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.id1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ht1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566508
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.ee1', '96.en1', '144.hg1', '144.px1', '144.pf1'], 'contains': ['576.dh1', '576.dk1', '576.dm1', '576.fi1', '576.fm1', '576.ge1', '576.gg1', '864.fc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 7621226, 87178328133, 2676], 'label': '6912.ia.288.jq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.ie1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566509
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.eo1', '144.hh1', '144.px1', '144.pf1'], 'contains': ['576.dh1', '576.dl1', '576.dm1', '576.fk1', '576.fp1', '576.gf1', '576.gh1', '864.fd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 6851, 87178328133, 83468087], 'label': '6912.ia.288.jr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.if1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566510
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.qj1', '96.ee1', '96.ep1', '144.hi1'], 'contains': ['576.di1', '576.dj1', '576.dn1', '576.fr1', '576.fs1', '576.gc1', '576.gj1', '864.fc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7656719, 7657413, 47537280, 87178328133], 'label': '6912.ia.288.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '288.ig1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.js1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566511
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dw1', '144.a1', '144.pl1', '144.pm1', '144.pn1'], 'contains': ['576.dp1', '576.ce1', '576.dd1', '576.dy1', '576.cj1', '864.eo1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 87178291200], 'label': '6912.ia.288.ir1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.ih1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ir1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566512
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ef1', '144.k1', '144.pl1', '144.qi1', '144.qj1', '144.qm1'], 'contains': ['576.dp1', '576.dq1', '576.du1', '576.ec1', '576.fg1', '864.ev1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 87178328133, 87091200], 'label': '6912.ia.288.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.ii1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566513
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.eg1', '144.l1', '144.pm1', '144.qi1', '144.qk1', '144.qn1'], 'contains': ['576.dp1', '576.dr1', '576.ds1', '576.dz1', '576.ef1', '576.fx1', '576.fy1', '864.ew1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87178328133, 40315919, 40279680], 'label': '6912.ia.288.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ij1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ju1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566514
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.eh1', '144.m1', '144.pm1', '144.qj1', '144.ql1', '144.qn1'], 'contains': ['576.dp1', '576.ds1', '576.ed1', '576.ek1', '576.fz1', '864.ex1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87105687, 87178328133, 40279680], 'label': '6912.ia.288.jv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ik1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566515
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ei1', '144.n1', '144.pn1', '144.qi1', '144.ql1', '144.qo1'], 'contains': ['576.dp1', '576.dt1', '576.ei1', '576.en1', '576.ga1', '864.ey1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 83476887, 87178328133, 87091200], 'label': '6912.ia.288.jw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.il1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566516
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.eg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ej1', '144.p1', '144.pl1', '144.qk1', '144.ql1', '144.qm1'], 'contains': ['576.dp1', '576.eq1', '576.er1', '864.ez1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 87178328133, 87091200], 'label': '6912.ia.288.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.im1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566517
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '12.bn1'], 'contains': ['48.h1', '48.i1', '48.k1', '48.cs1', '48.ct1', '48.o1', '48.q1', '48.x1', '48.bb1', '48.df1', '48.dg1', '48.fu1', '48.fj1', '72.d1', '72.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243566518
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ek1', '144.t1', '144.pn1', '144.qj1', '144.qk1', '144.qo1'], 'contains': ['576.dp1', '576.es1', '576.et1', '864.fa1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 43944719, 87178328133, 87091200], 'label': '6912.ia.288.jy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.in1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566519
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dm1', '144.k1', '144.pg1'], 'contains': ['576.ce1', '576.dq1', '576.cf1', '576.cn1', '576.fg1', '864.dz1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291200, 7657413, 87128133], 'label': '6912.ia.288.hu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '288.io1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566520
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dn1', '144.l1', '144.pm1', '144.pg1'], 'contains': ['576.ce1', '576.dr1', '576.ds1', '576.ck1', '576.cq1', '576.fx1', '576.fy1', '864.ea1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200, 40315919], 'label': '6912.ia.288.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ip1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566521
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.do1', '144.m1', '144.pm1', '144.ph1'], 'contains': ['576.ce1', '576.ds1', '576.co1', '576.cv1', '576.fz1', '864.eb1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200, 87105687], 'label': '6912.ia.288.hw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gr1', 'old_label': '288.iq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566522
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dp1', '144.n1', '144.pg1', '144.ph1'], 'contains': ['576.ce1', '576.dt1', '576.ct1', '576.cy1', '576.ga1', '864.ec1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87178291200, 87128133, 83476887], 'label': '6912.ia.288.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.ir1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566523
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.s1', '144.ph1'], 'contains': ['576.ce1', '576.db1', '576.dc1', '864.ed1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87128133, 43931924, 87178328133], 'label': '6912.ia.288.hy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '288.is1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566524
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.en1', '96.ep1', '144.hu1', '144.qi1', '144.pg1'], 'contains': ['576.dq1', '576.dr1', '576.dt1', '576.fh1', '576.fl1', '576.gb1', '576.gk1', '864.fc1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7656719, 93405312000, 7657413, 87178328133], 'label': '6912.ia.288.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.it1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566525
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eo1', '144.hv1', '144.qi1', '144.pg1'], 'contains': ['576.dq1', '576.ds1', '576.dt1', '576.fj1', '576.fo1', '576.gi1', '576.gl1', '864.fd1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [93405312000, 7657413, 83476887, 87178328133], 'label': '6912.ia.288.ka1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.iu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ka1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566526
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dx1', '144.fw1', '144.pl1', '144.po1', '144.pq1'], 'contains': ['576.dd1', '576.du1', '576.eq1', '864.ep1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 40316613, 93405312000, 127407813], 'label': '6912.ia.288.is1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.iv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.is1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566527
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dx1', '144.fx1', '144.pi1', '144.pp1', '144.pr1'], 'contains': ['576.de1', '576.dv1', '576.eu1', '864.ep1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 7657413, 2676, 127407813], 'label': '6912.ia.288.it1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.iw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.it1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566528
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '12.bn1'], 'contains': ['48.h1', '48.j1', '48.m1', '48.p1', '48.r1', '48.ba1', '48.bc1', '48.fv1', '72.e1', '72.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566529
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dx1', '144.fy1', '144.ps1'], 'contains': ['576.df1', '576.dw1', '576.ey1', '864.ep1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 40316613, 93405314676, 127407813], 'label': '6912.ia.288.iu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '288.ix1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566530
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dy1', '144.fz1', '144.pm1', '144.po1', '144.pt1'], 'contains': ['576.dd1', '576.dz1', '576.ed1', '576.ck1', '576.co1', '864.eq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 40315919], 'label': '6912.ia.288.iv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.iy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566531
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dy1', '144.gc1', '144.pj1', '144.pp1', '144.pu1'], 'contains': ['576.de1', '576.ea1', '576.ee1', '576.cl1', '576.cp1', '864.eq1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 127370880, 40280426, 2676], 'label': '6912.ia.288.iw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.iz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566532
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dz1', '144.gd1', '144.pi1', '144.pu1', '144.pv1'], 'contains': ['576.de1', '576.eb1', '576.ev1', '864.er1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 87185911680, 2676, 127407813], 'label': '6912.ia.288.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ja1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ix1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566533
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dz1', '144.ge1', '144.pl1', '144.pt1', '144.pw1'], 'contains': ['576.dd1', '576.ec1', '576.er1', '864.er1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40316613, 87185911680, 93405312000, 127407813], 'label': '6912.ia.288.iy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.jb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566534
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ea1', '144.gi1', '144.pm1', '144.pq1', '144.pw1'], 'contains': ['576.dd1', '576.ef1', '576.ek1', '576.cq1', '576.cv1', '864.es1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 87218607119], 'label': '6912.ia.288.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.iz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566535
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ea1', '144.gj1', '144.pj1', '144.pr1', '144.pv1'], 'contains': ['576.de1', '576.eg1', '576.el1', '576.cr1', '576.cw1', '864.es1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 127370880, 87218571626, 2676], 'label': '6912.ia.288.ja1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ja1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566536
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ea1', '144.gk1', '144.ps1'], 'contains': ['576.df1', '576.eh1', '576.em1', '576.cs1', '576.cx1', '864.es1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 127370880, 93405314676, 87218607119], 'label': '6912.ia.288.jb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.je1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566537
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.eb1', '144.gl1', '144.pn1', '144.po1', '144.pw1'], 'contains': ['576.dd1', '576.ei1', '576.es1', '864.et1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 43944719, 127407813], 'label': '6912.ia.288.jc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566538
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.eb1', '144.gm1', '144.pk1', '144.pp1', '144.pv1'], 'contains': ['576.de1', '576.ej1', '576.ew1', '864.et1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 43909226, 2676, 127407813], 'label': '6912.ia.288.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.jg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566539
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '12.bn1'], 'contains': ['48.i1', '48.l1', '48.m1', '48.y1', '48.z1', '48.bf1', '48.bg1', '48.fw1', '72.f1', '72.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243566540
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ec1', '144.gp1', '144.pn1', '144.pq1', '144.pt1'], 'contains': ['576.dd1', '576.en1', '576.et1', '864.eu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 87222235919, 127407813], 'label': '6912.ia.288.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.je1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566541
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ec1', '144.gq1', '144.pk1', '144.pr1', '144.pu1'], 'contains': ['576.de1', '576.eo1', '576.ex1', '864.eu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 87222200426, 2676, 127407813], 'label': '6912.ia.288.jf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ji1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566542
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ec1', '144.gs1', '144.ps1'], 'contains': ['576.df1', '576.ep1', '576.ez1', '864.eu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87222200426, 93405314676, 127407813], 'label': '6912.ia.288.jg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.jj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.jg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566543
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eq1', '144.u1', '144.pi1', '144.qb1', '144.qp1', '144.qq1'], 'contains': ['576.dv1', '576.dx1', '576.ev1', '864.fe1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 7657413, 2676, 87091200], 'label': '6912.ia.288.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566544
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eq1', '144.v1', '144.pl1', '144.qm1', '144.qr1', '144.qs1'], 'contains': ['576.du1', '576.dy1', '576.er1', '864.fe1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 87218607813, 93405312000, 87091200], 'label': '6912.ia.288.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.jl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566545
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.er1', '144.w1', '144.qi1', '144.po1', '144.qr1', '144.qx1'], 'contains': ['576.du1', '576.dz1', '576.ei1', '576.fh1', '576.fj1', '864.ff1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 7657413, 87091200, 83468087], 'label': '6912.ia.288.kd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566546
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.er1', '144.x1', '144.px1', '144.pp1', '144.qp1', '144.qy1'], 'contains': ['576.dv1', '576.ea1', '576.ej1', '576.fi1', '576.fk1', '864.ff1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 24536, 83476887, 87091200], 'label': '6912.ia.288.ke1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.jn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ke1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566547
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.es1', '144.y1', '144.qj1', '144.po1', '144.qs1', '144.qx1'], 'contains': ['576.du1', '576.ed1', '576.es1', '864.fg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 93405312000, 7657413, 87091200], 'label': '6912.ia.288.kf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566548
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.es1', '144.z1', '144.py1', '144.pp1', '144.qq1', '144.qy1'], 'contains': ['576.dv1', '576.ee1', '576.ew1', '864.fg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 43944719, 2676, 87091200], 'label': '6912.ia.288.kg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.jp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566549
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.et1', '144.ba1', '144.qi1', '144.pq1', '144.qs1', '144.qz1'], 'contains': ['576.du1', '576.ef1', '576.en1', '576.fl1', '576.fo1', '864.fh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 7657413, 87261759287, 87091200], 'label': '6912.ia.288.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566550
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '12.bn1'], 'contains': ['48.j1', '48.k1', '48.l1', '48.bd1', '48.be1', '48.bh1', '48.bi1', '48.fx1', '72.g1', '72.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566551
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.et1', '144.bb1', '144.px1', '144.pr1', '144.qq1', '144.ra1'], 'contains': ['576.dv1', '576.eg1', '576.eo1', '576.fm1', '576.fp1', '864.fh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 24536, 87261759287, 87091200], 'label': '6912.ia.288.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ki1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566552
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.et1', '144.bc1', '144.ps1', '144.rb1'], 'contains': ['576.dw1', '576.eh1', '576.ep1', '576.fn1', '576.fq1', '864.fh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 93405336536, 87261768087, 87091200], 'label': '6912.ia.288.kj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.js1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566553
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.eu1', '144.bd1', '144.qj1', '144.pq1', '144.qr1', '144.qz1'], 'contains': ['576.du1', '576.ek1', '576.et1', '864.fi1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 7657413, 87222200426, 87091200], 'label': '6912.ia.288.kk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.jt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566554
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eu1', '144.be1', '144.py1', '144.pr1', '144.qp1', '144.ra1'], 'contains': ['576.dv1', '576.el1', '576.ex1', '864.fi1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 87222235919, 2676, 87091200], 'label': '6912.ia.288.kl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ju1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566555
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.eu1', '144.bf1', '144.ps1', '144.rb1'], 'contains': ['576.dw1', '576.em1', '576.ez1', '864.fi1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87222235919, 93405314676, 87091200], 'label': '6912.ia.288.km1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.jv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.km1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566556
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ev1', '144.bk1', '144.pj1', '144.qe1', '144.qp1', '144.qt1'], 'contains': ['576.dx1', '576.ea1', '576.el1', '576.ft1', '576.fv1', '864.fj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40280426, 2676, 87305699013, 40279680], 'label': '6912.ia.288.kn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566557
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ew1', '144.bl1', '144.pi1', '144.qb1', '144.qt1', '144.qu1'], 'contains': ['576.dx1', '576.eb1', '576.eu1', '864.fk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 43908480, 2676, 87091200], 'label': '6912.ia.288.ko1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ko1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566558
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ex1', '144.bm1', '144.pj1', '144.qe1', '144.qq1', '144.qu1'], 'contains': ['576.dx1', '576.ee1', '576.eg1', '576.fu1', '576.fv1', '864.fl1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87305662080, 40304216, 87096887, 40279680], 'label': '6912.ia.288.kp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566559
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ey1', '144.bn1', '144.pk1', '144.qf1', '144.qp1', '144.qu1'], 'contains': ['576.dx1', '576.ej1', '576.ex1', '864.fm1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 24536, 87091200, 83468087], 'label': '6912.ia.288.kq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.jz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566560
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ez1', '144.bo1', '144.pk1', '144.qf1', '144.qq1', '144.qt1'], 'contains': ['576.dx1', '576.eo1', '576.ew1', '864.fn1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 43909226, 2676, 87091200], 'label': '6912.ia.288.kr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ka1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566561
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.j1', '12.l1', '12.o1', '12.r1', '12.t1', '12.bc1', '12.be1', '18.b1', '18.h1', '24.g1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 2676, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.6.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243566562
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.j1', '12.k1', '12.l1', '12.m1', '12.n1', '12.o1'], 'contains': ['48.d1', '48.bj1', '48.dr1', '72.h1', '72.bg1', '96.f1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.24.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566563
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ev1', '144.bp1', '144.pm1', '144.qn1', '144.qr1', '144.qv1'], 'contains': ['576.dy1', '576.dz1', '576.ek1', '576.fx1', '576.fz1', '864.fj1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 40315919, 87305699013, 40279680], 'label': '6912.ia.288.ks1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ks1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566564
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ew1', '144.bq1', '144.pl1', '144.qm1', '144.qv1', '144.qw1'], 'contains': ['576.dy1', '576.ec1', '576.eq1', '864.fk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218607813, 93405312000, 43908480, 87091200], 'label': '6912.ia.288.kt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.kc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566565
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ex1', '144.br1', '144.pm1', '144.qn1', '144.qs1', '144.qw1'], 'contains': ['576.dy1', '576.ed1', '576.ef1', '576.fy1', '576.fz1', '864.fl1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87105687, 87305699013, 40279680], 'label': '6912.ia.288.ku1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ku1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566566
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ey1', '144.bs1', '144.pn1', '144.qo1', '144.qr1', '144.qw1'], 'contains': ['576.dy1', '576.ei1', '576.et1', '864.fm1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218607813, 93405312000, 83476887, 87091200], 'label': '6912.ia.288.kv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ke1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566567
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ez1', '144.bt1', '144.pn1', '144.qo1', '144.qs1', '144.qv1'], 'contains': ['576.dy1', '576.en1', '576.es1', '864.fn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218607813, 93405312000, 43944719, 87091200], 'label': '6912.ia.288.kw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566568
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fa1', '144.by1', '144.qi1', '144.pt1', '144.qv1', '144.re1'], 'contains': ['576.dz1', '576.ec1', '576.en1', '576.gb1', '576.gi1', '864.fo1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87185948613, 87261759287, 87091200], 'label': '6912.ia.288.kx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566569
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fb1', '144.cd1', '144.qk1', '144.po1', '144.qv1', '144.qx1'], 'contains': ['576.dz1', '576.eq1', '576.es1', '864.fp1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 93405312000, 43945413, 87091200], 'label': '6912.ia.288.ky1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ky1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566570
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fc1', '144.ce1', '144.qk1', '144.pt1', '144.qr1', '144.re1'], 'contains': ['576.dz1', '576.er1', '576.et1', '864.fq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87222200426, 87222236613, 87091200], 'label': '6912.ia.288.kz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ki1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.kz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566571
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fa1', '144.cj1', '144.px1', '144.pu1', '144.qt1', '144.rh1'], 'contains': ['576.ea1', '576.eb1', '576.eo1', '576.ge1', '576.gf1', '864.fo1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 87261768087, 24536, 87091200], 'label': '6912.ia.288.la1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.kj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.la1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566572
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fb1', '144.ck1', '144.pz1', '144.pp1', '144.qt1', '144.qy1'], 'contains': ['576.ea1', '576.eu1', '576.ew1', '864.fp1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43908480, 43944719, 2676, 87091200], 'label': '6912.ia.288.lb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.kk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566573
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '8.b1', '12.bn1'], 'contains': ['48.h1', '48.l1', '48.bl1', '48.n1', '48.t1', '48.bn1', '48.bu1', '48.fk1', '48.fy1', '72.ir1', '72.ja1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.24.be1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243566574
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fc1', '144.cl1', '144.pz1', '144.pu1', '144.qp1', '144.rh1'], 'contains': ['576.ea1', '576.ev1', '576.ex1', '864.fq1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87222199680, 87222235919, 2676, 87091200], 'label': '6912.ia.288.lc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.kl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566575
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fd1', '144.cm1', '144.py1', '144.pu1', '144.qu1', '144.rh1'], 'contains': ['576.eb1', '576.ee1', '576.ex1', '864.fr1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 87222235919, 2676, 87091200], 'label': '6912.ia.288.ld1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.km1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ld1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566576
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fe1', '144.cn1', '144.px1', '144.pv1', '144.qu1', '144.ri1'], 'contains': ['576.eb1', '576.eg1', '576.ej1', '576.gg1', '576.gh1', '864.fs1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 24536, 83476887, 87091200], 'label': '6912.ia.288.le1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.kn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.le1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566577
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.ff1', '144.co1', '144.py1', '144.pv1', '144.qt1', '144.ri1'], 'contains': ['576.eb1', '576.el1', '576.ew1', '864.ft1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 43909226, 2676, 87091200], 'label': '6912.ia.288.lf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ko1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566578
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fd1', '144.cp1', '144.qj1', '144.pt1', '144.qw1', '144.re1'], 'contains': ['576.ec1', '576.ed1', '576.et1', '864.fr1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87222200426, 87185948613, 87091200], 'label': '6912.ia.288.lg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566579
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fe1', '144.cq1', '144.qi1', '144.pw1', '144.qw1', '144.rk1'], 'contains': ['576.ec1', '576.ef1', '576.ei1', '576.gk1', '576.gl1', '864.fs1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87185948613, 87091200, 83468087], 'label': '6912.ia.288.lh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566580
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ff1', '144.cr1', '144.qj1', '144.pw1', '144.qv1', '144.rk1'], 'contains': ['576.ec1', '576.ek1', '576.es1', '864.ft1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 93405312000, 87185948613, 87091200], 'label': '6912.ia.288.li1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.li1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566581
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fg1', '144.cx1', '144.ql1', '144.po1', '144.qw1', '144.qx1'], 'contains': ['576.ed1', '576.ei1', '576.eq1', '864.fu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 43945413, 87091200, 83468087], 'label': '6912.ia.288.lj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ks1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566582
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fh1', '144.da1', '144.ql1', '144.pt1', '144.qs1', '144.re1'], 'contains': ['576.ed1', '576.en1', '576.er1', '864.fv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87222236613, 87261759287, 87091200], 'label': '6912.ia.288.lk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566583
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fg1', '144.df1', '144.qa1', '144.pp1', '144.qu1', '144.qy1'], 'contains': ['576.ee1', '576.ej1', '576.eu1', '864.fu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43908480, 24536, 83476887, 87091200], 'label': '6912.ia.288.ll1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.ku1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ll1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566584
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '12.bo1', '12.bq1', '12.br1'], 'contains': ['48.a1', '48.bq1', '48.bx1', '48.fz1', '72.it1', '72.jb1', '96.be1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bf1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566585
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fh1', '144.dg1', '144.qa1', '144.pu1', '144.qq1', '144.rh1'], 'contains': ['576.ee1', '576.eo1', '576.ev1', '864.fv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87222199680, 87261768087, 24536, 87091200], 'label': '6912.ia.288.lm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.kv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566586
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fi1', '144.dj1', '144.qk1', '144.pq1', '144.qw1', '144.qz1'], 'contains': ['576.ef1', '576.eq1', '576.et1', '864.fw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 43945413, 87222200426, 87091200], 'label': '6912.ia.288.ln1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ln1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566587
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fj1', '144.dk1', '144.qk1', '144.pw1', '144.qs1', '144.rk1'], 'contains': ['576.ef1', '576.er1', '576.es1', '864.fx1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 93405312000, 87222236613, 87091200], 'label': '6912.ia.288.lo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.kx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566588
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fi1', '144.dn1', '144.pz1', '144.pr1', '144.qu1', '144.ra1'], 'contains': ['576.eg1', '576.eu1', '576.ex1', '864.fw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [43908480, 87222235919, 2676, 87091200], 'label': '6912.ia.288.lp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ky1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566589
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fj1', '144.do1', '144.pz1', '144.pv1', '144.qq1', '144.ri1'], 'contains': ['576.eg1', '576.ev1', '576.ew1', '864.fx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87222199680, 43944719, 2676, 87091200], 'label': '6912.ia.288.lq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.kz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566590
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fi1', '144.dp1', '144.ps1', '144.rb1'], 'contains': ['576.eh1', '576.ey1', '576.ez1', '864.fw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [43908480, 87222235919, 93405314676, 87091200], 'label': '6912.ia.288.lr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.la1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566591
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fk1', '144.ds1', '144.ql1', '144.pw1', '144.qr1', '144.rk1'], 'contains': ['576.ei1', '576.ek1', '576.er1', '864.fy1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87222236613, 87091200, 83468087], 'label': '6912.ia.288.ls1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.lb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ls1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566592
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fk1', '144.dy1', '144.qa1', '144.pv1', '144.qp1', '144.ri1'], 'contains': ['576.ej1', '576.el1', '576.ev1', '864.fy1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87222199680, 24536, 87091200, 83468087], 'label': '6912.ia.288.lt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.lc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566593
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fl1', '144.dz1', '144.ql1', '144.pq1', '144.qv1', '144.qz1'], 'contains': ['576.ek1', '576.en1', '576.eq1', '864.fz1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 43945413, 87261759287, 87091200], 'label': '6912.ia.288.lu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.ld1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566594
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fl1', '144.eb1', '144.qa1', '144.pr1', '144.qt1', '144.ra1'], 'contains': ['576.el1', '576.eo1', '576.eu1', '864.fz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [43908480, 87261768087, 24536, 87091200], 'label': '6912.ia.288.lv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.le1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566595
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '8.c1', '12.bn1'], 'contains': ['48.i1', '48.j1', '48.bl1', '48.s1', '48.u1', '48.br1', '48.ca1', '48.fl1', '48.ga1', '72.iu1', '72.jb1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.24.bg1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '24.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243566596
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.fl1', '144.ec1', '144.ps1', '144.rb1'], 'contains': ['576.em1', '576.ep1', '576.ey1', '864.fz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [43908480, 93405336536, 87261768087, 87091200], 'label': '6912.ia.288.lw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.lf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566597
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '96.fm1', '144.fw1', '144.qm1', '144.qx1', '144.qz1'], 'contains': ['576.b1', '576.du1', '576.eq1', '864.ga1'], 'core': '576.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 40279680], 'label': '6912.ia.288.lx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.lg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566598
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fm1', '96.fn1', '144.fx1', '144.qb1', '144.qy1', '144.ra1'], 'contains': ['576.dv1', '576.eu1', '576.fa1', '864.ga1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 7657413, 2676, 40279680], 'label': '6912.ia.288.ly1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.lh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ly1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566599
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fm1', '96.fo1', '144.fy1', '144.rb1'], 'contains': ['576.dw1', '576.ey1', '576.fb1', '864.ga1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 7657413, 93405314676, 40279680], 'label': '6912.ia.288.lz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '288.li1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.lz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566600
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fp1', '96.fq1', '144.fz1', '144.qn1', '144.qx1', '144.re1'], 'contains': ['576.b1', '576.dz1', '576.ed1', '864.gb1'], 'core': '576.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 40279680], 'label': '6912.ia.288.ma1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '288.lj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ma1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566601
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fp1', '96.fr1', '144.ga1', '144.qd1', '144.rc1', '144.rf1'], 'contains': ['576.c1', '864.gb1', '1152.y1'], 'core': '576.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 40280426, 47537280, 40279680], 'label': '6912.ia.288.mb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '288.lk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566602
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fp1', '96.fs1', '144.gb1', '144.rg1'], 'contains': ['576.fc1', '864.gb1', '1152.z1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 40280426, 93452849280, 40279680], 'label': '6912.ia.288.mc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bv1', 'old_label': '288.ll1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566603
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fq1', '96.fr1', '96.fs1', '144.gc1', '144.qe1', '144.qy1', '144.rh1'], 'contains': ['576.ea1', '576.ee1', '576.fa1', '864.gb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 40315919, 2676, 40279680], 'label': '6912.ia.288.md1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '288.lm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.md1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566604
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ft1', '96.fu1', '96.fv1', '144.gd1', '144.qb1', '144.rh1', '144.ri1'], 'contains': ['576.eb1', '576.ev1', '576.fa1', '864.gc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 87185948613, 2676, 40279680], 'label': '6912.ia.288.me1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ln1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.me1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566605
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.ft1', '144.ge1', '144.qm1', '144.re1', '144.rk1'], 'contains': ['576.b1', '576.ec1', '576.er1', '864.gc1'], 'core': '576.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 87185948613, 40279680], 'label': '6912.ia.288.mf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.lo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566606
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1', '8.d1', '12.bn1'], 'contains': ['48.k1', '48.m1', '48.bl1', '48.v1', '48.w1', '48.cb1', '48.cf1', '48.fm1', '48.gb1', '72.iv1', '72.jc1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.24.bh1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566607
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.fu1', '144.gf1', '144.qc1', '144.rf1', '144.rj1'], 'contains': ['576.c1', '864.gc1', '1152.bd1'], 'core': '576.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 47537280, 87185948613, 40279680], 'label': '6912.ia.288.mg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.lp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566608
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.fv1', '144.gg1', '144.rg1'], 'contains': ['576.fc1', '864.gc1', '1152.be1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87185948613, 93452849280, 40279680], 'label': '6912.ia.288.mh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '288.lq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566609
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fw1', '96.fx1', '96.fy1', '144.gh1', '144.qd1', '144.rd1', '144.rj1'], 'contains': ['576.c1', '864.gd1', '1152.bh1'], 'core': '576.c1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 47537280, 87218571626, 40279680], 'label': '6912.ia.288.mi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '288.lr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566610
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fw1', '96.fz1', '144.gi1', '144.qn1', '144.qz1', '144.rk1'], 'contains': ['576.b1', '576.ef1', '576.ek1', '864.gd1'], 'core': '576.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 87218571626, 40279680], 'label': '6912.ia.288.mj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '288.ls1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566611
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fx1', '96.fz1', '144.gj1', '144.qe1', '144.ra1', '144.ri1'], 'contains': ['576.eg1', '576.el1', '576.fa1', '864.gd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 2676, 87218607119, 40279680], 'label': '6912.ia.288.mk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '288.lt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566612
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fy1', '96.fz1', '144.gk1', '144.rb1'], 'contains': ['576.eh1', '576.em1', '576.fb1', '864.gd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 93405314676, 87218607119, 40279680], 'label': '6912.ia.288.ml1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '288.lu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ml1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566613
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ga1', '96.gb1', '96.gc1', '144.gl1', '144.qo1', '144.qx1', '144.rk1'], 'contains': ['576.b1', '576.ei1', '576.es1', '864.ge1'], 'core': '576.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 40279680], 'label': '6912.ia.288.mm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.lv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566614
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ga1', '96.gd1', '144.gm1', '144.qf1', '144.qy1', '144.ri1'], 'contains': ['576.ej1', '576.ew1', '576.fa1', '864.ge1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 43944719, 2676, 40279680], 'label': '6912.ia.288.mn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.lw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566615
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.gb1', '96.gd1', '144.gn1', '144.qg1', '144.rc1', '144.rj1'], 'contains': ['576.c1', '864.ge1', '1152.bn1'], 'core': '576.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 43909226, 47537280, 40279680], 'label': '6912.ia.288.mo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '288.lx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566616
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gc1', '96.gd1', '144.go1', '144.qh1'], 'contains': ['576.fd1', '864.ge1', '1152.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120116474, 127370880, 43944719, 40279680], 'label': '6912.ia.288.mp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '288.ly1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566617
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '12.bo1', '12.bq1', '12.bs1'], 'contains': ['48.a1', '48.cc1', '48.cg1', '48.gc1', '72.iw1', '72.jc1', '96.bi1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bi1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566618
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ge1', '96.gf1', '96.gg1', '144.gp1', '144.qo1', '144.qz1', '144.re1'], 'contains': ['576.b1', '576.en1', '576.et1', '864.gf1'], 'core': '576.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 40279680], 'label': '6912.ia.288.mq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '288.lz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566619
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ge1', '96.gh1', '96.gi1', '144.gq1', '144.qf1', '144.ra1', '144.rh1'], 'contains': ['576.eo1', '576.ex1', '576.fa1', '864.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 87222235919, 2676, 40279680], 'label': '6912.ia.288.mr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '288.ma1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566620
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ms1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.gf1', '96.gh1', '96.gj1', '144.gr1', '144.qg1', '144.rd1', '144.rf1'], 'contains': ['576.c1', '864.gf1', '1152.bu1'], 'core': '576.c1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87222200426, 47537280, 40279680], 'label': '6912.ia.288.ms1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '288.mb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ms1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566621
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ge1', '96.gj1', '96.gk1', '144.gs1', '144.rb1'], 'contains': ['576.ep1', '576.ez1', '576.fb1', '864.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [127370880, 87222235919, 93405314676, 40279680], 'label': '6912.ia.288.mt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '288.mc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566622
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.gf1', '96.gi1', '96.gk1', '144.gt1', '144.rg1'], 'contains': ['576.fc1', '864.gf1', '1152.bw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 87222200426, 93452849280, 40279680], 'label': '6912.ia.288.mu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.js1', 'old_label': '288.md1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566623
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gg1', '96.gh1', '96.gk1', '144.gu1', '144.qh1'], 'contains': ['576.fd1', '864.gf1', '1152.bx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [120116474, 127370880, 87222235919, 40279680], 'label': '6912.ia.288.mv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ix1', 'old_label': '288.me1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566624
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gg1', '96.gi1', '96.gj1', '96.gk1', '144.gv1'], 'contains': ['576.fe1', '864.gf1', '1152.by1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [127370880, 93525428474, 87222235919, 40279680], 'label': '6912.ia.288.mw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.gv1', 'old_label': '288.mf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566625
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dq1', '144.w1', '144.pg1'], 'contains': ['576.cf1', '576.ck1', '576.ct1', '576.fh1', '576.fj1', '864.ee1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 93405312000, 87128133, 83476887], 'label': '6912.ia.288.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.mg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.hz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566626
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dq1', '144.x1', '144.pf1'], 'contains': ['576.cg1', '576.cl1', '576.cu1', '576.fi1', '576.fk1', '864.ee1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7657413, 24536, 87128133, 83476887], 'label': '6912.ia.288.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '288.mh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ia1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566627
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dr1', '144.ba1', '144.pg1'], 'contains': ['576.cf1', '576.cq1', '576.cy1', '576.fl1', '576.fo1', '864.ef1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 93405312000, 87261768087, 87128133], 'label': '6912.ia.288.ib1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.mi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ib1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566628
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1', '8.d1'], 'contains': ['48.bm1', '48.cd1', '48.ch1', '48.gd1', '72.ix1', '72.jc1', '96.bj1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.24.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '24.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566629
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dr1', '144.bb1', '144.pf1'], 'contains': ['576.cg1', '576.cr1', '576.cz1', '576.fm1', '576.fp1', '864.ef1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7657413, 87261768087, 24536, 87128133], 'label': '6912.ia.288.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.mj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ic1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566630
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dr1', '144.bc1'], 'contains': ['576.ch1', '576.cs1', '576.da1', '576.fn1', '576.fq1', '864.ef1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [93405336536, 7657413, 87261768087, 87128133], 'label': '6912.ia.288.id1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '288.mk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.id1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566631
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ds1', '144.bk1', '144.pj1'], 'contains': ['576.ci1', '576.cl1', '576.cw1', '576.ft1', '576.fv1', '864.eg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 40315919, 2676, 87305699013], 'label': '6912.ia.288.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '288.ml1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ie1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566632
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dt1', '144.bm1', '144.pj1'], 'contains': ['576.ci1', '576.cp1', '576.cr1', '576.fu1', '576.fv1', '864.eh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87305662080, 87105687, 40310618], 'label': '6912.ia.288.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '288.mm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.if1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566633
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ds1', '144.bp1', '144.pm1'], 'contains': ['576.cj1', '576.ck1', '576.cv1', '576.fx1', '576.fz1', '864.eg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 40280426, 87305699013], 'label': '6912.ia.288.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jb1', 'old_label': '288.mn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ig1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566634
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dt1', '144.br1', '144.pm1'], 'contains': ['576.cj1', '576.co1', '576.cq1', '576.fy1', '576.fz1', '864.eh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 93405312000, 87096887, 87305699013], 'label': '6912.ia.288.ih1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jb1', 'old_label': '288.mo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ih1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566635
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.du1', '144.by1', '144.pg1'], 'contains': ['576.ck1', '576.cn1', '576.cy1', '576.gb1', '576.gi1', '864.ei1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 93405312000, 87261768087, 87128133], 'label': '6912.ia.288.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.mp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ii1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566636
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.du1', '144.cj1', '144.pf1'], 'contains': ['576.cl1', '576.cm1', '576.cz1', '576.ge1', '576.gf1', '864.ei1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [24536, 87185948613, 87261768087, 87128133], 'label': '6912.ia.288.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.mq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ij1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566637
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.dv1', '144.cn1', '144.pf1'], 'contains': ['576.cm1', '576.cr1', '576.cu1', '576.gg1', '576.gh1', '864.ej1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185948613, 24536, 87128133, 83476887], 'label': '6912.ia.288.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.mr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ik1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566638
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.dv1', '144.cq1', '144.pg1'], 'contains': ['576.cn1', '576.cq1', '576.ct1', '576.gk1', '576.gl1', '864.ej1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 93405312000, 87128133, 83476887], 'label': '6912.ia.288.il1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.ms1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.il1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566639
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.bp1', '12.br1', '12.bs1', '12.bt1', '12.bu1', '12.bv1'], 'contains': ['48.a1', '48.cm1', '48.cn1', '72.iy1', '72.jd1', '96.bk1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566640
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cy1', '144.ph1'], 'contains': ['576.co1', '576.ct1', '576.db1', '864.ek1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [119759865, 93405312000, 87128133, 83468087], 'label': '6912.ia.288.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '288.mt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.im1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566641
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '144.ph1'], 'contains': ['576.co1', '576.cy1', '576.dc1', '864.el1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87298051065, 93405312000, 87128133, 87261759287], 'label': '6912.ia.288.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '288.mu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.in1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566642
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dt1', '144.ph1'], 'contains': ['576.ct1', '576.cv1', '576.dc1', '864.em1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87298051065, 93405312000, 87128133, 83468087], 'label': '6912.ia.288.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '288.mv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.io1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243566644
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.gl1', '144.io1', '144.px1', '144.pf1'], 'contains': ['576.ff1', '576.fi1', '576.fp1', '576.ft1', '576.fw1', '576.ge1', '576.gh1', '864.gg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 7621226, 87265419333, 2676], 'label': '6912.ia.288.mx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.mx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566645
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.my1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.gm1', '144.ip1', '144.px1', '144.pf1'], 'contains': ['576.ff1', '576.fk1', '576.fm1', '576.fu1', '576.fw1', '576.gf1', '576.gg1', '864.gh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 6851, 87265419333, 83468087], 'label': '6912.ia.288.my1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '288.my1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.my1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566646
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.mz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.gl1', '144.iq1', '144.qi1', '144.pg1'], 'contains': ['576.fg1', '576.fh1', '576.fo1', '576.fx1', '576.ga1', '576.gb1', '576.gl1', '864.gg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7656719, 93405312000, 7657413, 87265419333], 'label': '6912.ia.288.mz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.mz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.mz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566647
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '288.na1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.gm1', '144.ir1', '144.qi1', '144.pg1'], 'contains': ['576.fg1', '576.fj1', '576.fl1', '576.fy1', '576.ga1', '576.gi1', '576.gk1', '864.gh1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 93405312000, 83476887, 87265419333], 'label': '6912.ia.288.na1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '288.na1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.na1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566648
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '128.a1', '192.d1', '192.b1', '192.g1', '192.k1', '192.m1', '192.p1', '192.t1', '192.x1', '192.y1', '192.bc1', '192.bd1'], 'contains': ['768.a1', '1152.a1', '1152.c1', '1152.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 36933, 2676], 'label': '6912.ia.384.a1', 'mobius_quo': None, 'mobius_sub': 96, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '384.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566649
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '128.a1', '192.e1', '192.h1', '192.l1', '192.s1', '192.u1', '192.z1', '192.be1', '192.bk1', '192.bl1', '192.bm1', '192.bn1'], 'contains': ['768.b1', '1152.a1', '1152.d1', '1152.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 47537280, 36933], 'label': '6912.ia.384.b1', 'mobius_quo': None, 'mobius_sub': 96, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '384.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566650
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '12.bq1', '12.bt1'], 'contains': ['48.a1', '48.co1', '48.cp1', '72.iz1', '72.je1', '96.bl1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43941409, 127370880, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.24.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566651
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.u1', '96.dg1', '96.dh1', '128.a1', '192.f1', '192.ba1', '192.bf1'], 'contains': ['768.c1', '1152.a1', '1152.g1', '1152.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120116474, 93405312000, 36933], 'label': '6912.ia.384.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '384.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566652
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.v1', '96.di1', '128.a1', '192.c1', '192.i1', '192.n1', '192.q1', '192.v1', '192.bb1', '192.bg1'], 'contains': ['768.d1', '1152.c1', '1152.d1', '1152.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 47537280, 36933], 'label': '6912.ia.384.d1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '384.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566653
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1', '96.dj1', '128.a1', '192.o1', '192.r1', '192.bh1'], 'contains': ['768.e1', '1152.c1', '1152.f1', '1152.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [174404119680, 93525427956, 36933], 'label': '6912.ia.384.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '384.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566654
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.x1', '96.dk1', '128.a1', '192.j1', '192.w1', '192.bi1'], 'contains': ['768.f1', '1152.d1', '1152.e1', '1152.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [93525427956, 47537280, 36933], 'label': '6912.ia.384.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '384.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566655
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1', '96.dl1', '128.a1', '192.bj1'], 'contains': ['768.g1', '1152.e1', '1152.f1', '1152.g1', '1152.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120115956, 93452849280, 36933], 'label': '6912.ia.384.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.g1', 'old_label': '384.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566656
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ed1', '128.b1', '192.c1', '192.bz1', '192.ca1', '192.cb1'], 'contains': ['768.d1', '1152.l1', '1152.m1', '1152.n1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120115956, 47537280, 87178328133], 'label': '6912.ia.384.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '384.h1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566657
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.b1', '192.d1', '192.cc1', '192.bo1', '192.cd1', '192.cg1', '192.ch1', '192.ci1'], 'contains': ['768.a1', '1152.b1', '1152.l1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405312000, 87178328133, 2676], 'label': '6912.ia.384.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '384.i1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566658
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.dy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '128.b1', '192.e1', '192.ce1', '192.cf1', '192.cj1'], 'contains': ['768.b1', '1152.b1', '1152.m1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405312000, 47537280, 87178328133], 'label': '6912.ia.384.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '384.j1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566659
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.em1', '128.b1', '192.f1', '192.ck1'], 'contains': ['768.c1', '1152.b1', '1152.n1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120116474, 93405312000, 87178328133], 'label': '6912.ia.384.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '384.k1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566660
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1', '192.cc1', '192.by1', '192.cl1', '192.cm1', '192.cn1', '192.co1', '192.cp1', '192.cq1', '192.cr1', '192.cs1', '192.ct1', '192.cu1', '192.cv1', '192.cw1', '192.cx1', '192.cy1'], 'contains': ['768.a1', '1152.o1', '1152.p1', '1152.q1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 2676, 40279680], 'label': '6912.ia.384.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '384.l1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566661
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '12.j1', '12.dq1', '12.dr1'], 'contains': ['48.d1', '48.dh1', '48.ea1', '72.lw1', '72.mp1', '96.bc1'], 'core': '48.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 87178291200, 36933, 2676], 'label': '6912.ia.24.dd1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566662
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1', '192.bo1', '192.by1', '192.bp1', '192.bq1', '192.br1', '192.bs1', '192.bt1', '192.bu1', '192.bv1', '192.bw1', '192.bx1'], 'contains': ['768.a1', '1152.i1', '1152.j1', '1152.k1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40316613, 93405312000, 2676], 'label': '6912.ia.384.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '384.m1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566663
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.c1', '192.g1', '192.cd1', '192.cl1', '192.bp1', '192.de1', '192.df1', '192.dg1', '192.dh1', '192.di1'], 'contains': ['768.a1', '1152.r1', '1152.s1', '1152.t1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 7657413, 2676], 'label': '6912.ia.384.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '384.n1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566666
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fo1', '128.c1', '192.j1', '192.dn1'], 'contains': ['768.f1', '1152.t1', '1152.u1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [7620480, 93525427956, 47537280], 'label': '6912.ia.384.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '384.q1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566667
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.k1', '192.cc1', '192.bo1', '192.cm1', '192.bq1', '192.de1', '192.do1', '192.dp1', '192.dq1', '192.dr1'], 'contains': ['768.a1', '1152.v1', '1152.w1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87218607813, 93405312000, 2676], 'label': '6912.ia.384.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '384.r1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566668
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fp1', '128.d1', '192.l1', '192.cf1', '192.dj1', '192.ds1'], 'contains': ['768.b1', '1152.x1', '1152.y1', '1152.z1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 47537280, 746], 'label': '6912.ia.384.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '384.s1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566669
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.d1', '192.m1', '192.cg1', '192.cn1', '192.br1', '192.df1', '192.do1', '192.dt1'], 'contains': ['768.a1', '1152.x1', '1152.ba1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36239, 93405312000, 2676], 'label': '6912.ia.384.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '384.t1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566670
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fr1', '128.d1', '192.n1', '192.ca1', '192.dk1', '192.du1'], 'contains': ['768.d1', '1152.y1', '1152.ba1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 47537280, 746], 'label': '6912.ia.384.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '384.u1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566671
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fs1', '128.d1', '192.o1', '192.dv1'], 'contains': ['768.e1', '1152.z1', '1152.ba1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [174404119680, 93525427956, 746], 'label': '6912.ia.384.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '384.v1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566672
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.k1', '12.n1', '12.o1', '12.ba1', '12.bb1', '12.bh1', '12.bi1', '18.c1', '18.j1', '24.h1'], 'core': '24.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 43908480, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.6.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566673
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '12.ds1'], 'contains': ['48.cu1', '48.cv1', '48.cw1', '48.cx1', '48.cy1', '48.di1', '48.dj1', '48.dk1', '48.ds1', '48.dt1', '48.ed1', '72.lx1', '72.mk1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.24.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243566674
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.e1', '192.p1', '192.cd1', '192.co1', '192.bs1', '192.de1', '192.dt1', '192.dw1', '192.dy1', '192.dz1'], 'contains': ['768.a1', '1152.bb1', '1152.bc1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 87185948613, 2676], 'label': '6912.ia.384.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '384.w1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566675
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fu1', '128.e1', '192.q1', '192.bz1', '192.du1', '192.dx1'], 'contains': ['768.d1', '1152.bb1', '1152.bd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120115956, 47537280, 87185948613], 'label': '6912.ia.384.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '384.x1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566676
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fv1', '128.e1', '192.r1', '192.dv1'], 'contains': ['768.e1', '1152.bb1', '1152.be1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [174404119680, 93525427956, 87185948613], 'label': '6912.ia.384.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '384.y1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566677
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '128.e1', '192.s1', '192.ce1', '192.ds1', '192.ea1'], 'contains': ['768.b1', '1152.bc1', '1152.bd1', '1152.be1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405312000, 47537280, 87185948613], 'label': '6912.ia.384.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '384.z1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.z1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566678
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.t1', '192.ch1', '192.cn1', '192.cp1', '192.br1', '192.bt1', '192.dg1', '192.dp1', '192.dq1', '192.dw1'], 'contains': ['768.a1', '1152.bf1', '1152.bg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 40315919, 2676], 'label': '6912.ia.384.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '384.ba1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566679
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.fw1', '128.f1', '192.u1', '192.cf1', '192.dl1', '192.ea1'], 'contains': ['768.b1', '1152.bh1', '1152.bi1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 47537280, 87178291946], 'label': '6912.ia.384.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '384.bb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566680
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fx1', '128.f1', '192.v1', '192.ca1', '192.dm1', '192.dx1'], 'contains': ['768.d1', '1152.bh1', '1152.bj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120115956, 87178327439, 47537280], 'label': '6912.ia.384.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '384.bc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566681
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.fy1', '128.f1', '192.w1', '192.dn1'], 'contains': ['768.f1', '1152.bh1', '1152.bk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [93525427956, 87178327439, 47537280], 'label': '6912.ia.384.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '384.bd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566682
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.f1', '192.x1', '192.cg1', '192.cq1', '192.bu1', '192.dh1', '192.dp1', '192.dy1'], 'contains': ['768.a1', '1152.bi1', '1152.bj1', '1152.bk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405312000, 2676, 87178291946], 'label': '6912.ia.384.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '384.be1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.be1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566683
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.g1', '192.y1', '192.ci1', '192.cr1', '192.bv1', '192.df1', '192.dg1', '192.dr1', '192.dy1', '192.dz1'], 'contains': ['768.a1', '1152.bl1', '1152.bm1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6851, 93405312000, 83468087], 'label': '6912.ia.384.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '384.bf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566684
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '12.ds1'], 'contains': ['48.cv1', '48.da1', '48.db1', '48.dm1', '48.dn1', '48.ef1', '48.eg1', '72.ly1', '72.mn1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 7654690, 47537280, 36933], 'label': '6912.ia.24.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243566685
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.gb1', '128.g1', '192.z1', '192.cj1', '192.dj1', '192.ea1'], 'contains': ['768.b1', '1152.bl1', '1152.bn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 79833600, 83468087], 'label': '6912.ia.384.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '384.bg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566686
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gc1', '128.g1', '192.ba1', '192.ck1'], 'contains': ['768.c1', '1152.bl1', '1152.bo1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [93405312000, 43561327, 83468087], 'label': '6912.ia.384.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '384.bh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566687
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gd1', '128.g1', '192.bb1', '192.cb1', '192.dk1', '192.dx1'], 'contains': ['768.d1', '1152.bm1', '1152.bn1', '1152.bo1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [43570136, 79833600, 83476887], 'label': '6912.ia.384.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '384.bi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566688
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.bc1', '192.ch1', '192.cq1', '192.cs1', '192.bu1', '192.bw1', '192.di1', '192.do1', '192.dq1', '192.dz1'], 'contains': ['768.a1', '1152.bp1', '1152.bq1', '1152.br1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 2676, 87218607119], 'label': '6912.ia.384.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '384.bj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566689
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.h1', '192.bd1', '192.ci1', '192.ct1', '192.bx1', '192.dh1', '192.di1', '192.dr1', '192.dt1', '192.dw1'], 'contains': ['768.a1', '1152.bs1', '1152.bt1', '1152.bv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6851, 93405312000, 87261768087], 'label': '6912.ia.384.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '384.bk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566690
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.gf1', '128.h1', '192.be1', '192.cj1', '192.dl1', '192.ds1'], 'contains': ['768.b1', '1152.bs1', '1152.bu1', '1152.bw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93405312000, 79833600, 87261759287], 'label': '6912.ia.384.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '384.bl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566691
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gg1', '128.h1', '192.bf1', '192.ck1'], 'contains': ['768.c1', '1152.bs1', '1152.bx1', '1152.by1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [93405312000, 43561327, 87261759287], 'label': '6912.ia.384.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '384.bm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566692
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gh1', '128.h1', '192.bg1', '192.cb1', '192.dm1', '192.du1'], 'contains': ['768.d1', '1152.bt1', '1152.bu1', '1152.bx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [43570136, 79833600, 87261759287], 'label': '6912.ia.384.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '384.bn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566693
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gi1', '128.h1', '192.bh1', '192.dv1'], 'contains': ['768.e1', '1152.bt1', '1152.bw1', '1152.by1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [93448882136, 87261768087, 174436416000], 'label': '6912.ia.384.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cj1', 'old_label': '384.bo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566694
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gj1', '128.h1', '192.bi1', '192.dn1'], 'contains': ['768.f1', '1152.bu1', '1152.bv1', '1152.by1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [93448882136, 79833600, 87261759287], 'label': '6912.ia.384.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bv1', 'old_label': '384.bp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243566695
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '8.i1', '12.ds1'], 'contains': ['48.cv1', '48.cz1', '48.dc1', '48.dl1', '48.do1', '48.ee1', '48.eh1', '72.lz1', '72.mp1'], 'core': '144.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.24.dg1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '24.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243566696
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '384.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.gk1', '128.h1', '192.bj1'], 'contains': ['768.g1', '1152.bv1', '1152.bw1', '1152.bx1', '1152.by1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [43570136, 93485145600, 87261768087], 'label': '6912.ia.384.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.bj1', 'old_label': '384.bq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.bq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 243566697
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '144.k1', '216.b1', '216.c1', '216.d1', '216.e1', '216.hn1'], 'contains': ['864.c1', '864.y1', '864.d1', '864.g1', '864.bf1', '864.ev1', '864.dz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 87091200], 'label': '6912.ia.432.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566698
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1', '144.l1', '216.b1', '216.f1', '216.g1', '216.h1', '216.i1', '216.j1', '216.ho1'], 'contains': ['864.c1', '864.z1', '864.ba1', '864.f1', '864.i1', '864.bo1', '864.bp1', '864.ew1', '864.ea1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.432.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566699
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1', '144.m1', '216.c1', '216.i1', '216.k1', '216.l1', '216.m1', '216.n1', '216.ho1'], 'contains': ['864.c1', '864.ba1', '864.h1', '864.k1', '864.bq1', '864.ex1', '864.eb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 36933, 87096887, 40279680], 'label': '6912.ia.432.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566700
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1', '144.n1', '216.b1', '216.f1', '216.k1', '216.l1', '216.o1', '216.p1', '216.hp1'], 'contains': ['864.c1', '864.bb1', '864.j1', '864.l1', '864.br1', '864.ey1', '864.ec1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.432.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566701
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '216.d1', '216.j1', '216.n1', '216.p1', '216.q1', '216.s1', '216.r1', '216.t1', '216.u1', '216.v1', '216.w1', '216.x1', '216.y1', '216.z1', '216.hq1'], 'contains': ['864.c1', '864.bc1', '864.bd1', '864.m1', '864.p1', '864.bs1', '864.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 32929, 87178291200, 36933], 'label': '6912.ia.432.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566702
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.i1', '144.p1', '216.g1', '216.k1', '216.q1', '216.ba1', '216.hn1'], 'contains': ['864.c1', '864.n1', '864.q1', '864.ez1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43908480, 87178291200, 36933, 87091200], 'label': '6912.ia.432.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566703
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '216.e1', '216.i1', '216.o1', '216.y1', '216.ba1', '216.bb1', '216.hq1'], 'contains': ['864.c1', '864.bd1', '864.o1', '864.t1', '864.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 87178291200, 36933, 87100665], 'label': '6912.ia.432.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566704
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '216.e1', '216.h1', '216.l1', '216.q1', '216.s1', '216.bb1', '216.hr1'], 'contains': ['864.c1', '864.s1', '864.w1', '864.ed1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 87178291200, 36933, 87091200], 'label': '6912.ia.432.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566705
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1', '216.d1', '216.f1', '216.m1', '216.r1', '216.ba1', '216.bb1', '216.hr1'], 'contains': ['864.c1', '864.be1', '864.r1', '864.v1', '864.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7653409, 87178291200, 36933, 87091200], 'label': '6912.ia.432.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566725
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ij1', '216.u1', '216.v1', '216.ix1', '216.iz1', '216.jd1', '216.jf1', '216.jj1'], 'contains': ['864.bc1', '864.dl1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178291200, 40313890, 36933], 'label': '6912.ia.432.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566706
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '12.ds1'], 'contains': ['48.cx1', '48.cz1', '48.db1', '48.dv1', '48.dw1', '48.ek1', '48.el1', '72.ma1', '72.mr1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.24.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243566707
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1', '144.t1', '216.c1', '216.g1', '216.h1', '216.m1', '216.o1', '216.t1', '216.hp1'], 'contains': ['864.c1', '864.u1', '864.x1', '864.fa1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 87178291200, 36933, 87091200], 'label': '6912.ia.432.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566708
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.ft1', '144.fu1', '144.fv1', '216.hn1', '216.ho1', '216.hp1', '216.hq1', '216.hr1'], 'contains': ['864.a1', '864.c1', '864.e1', '864.eo1', '864.fb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87178291200, 36933, 40279680], 'label': '6912.ia.432.eh1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566709
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hg1', '144.hi1', '144.hu1', '216.b1', '216.is1', '216.it1'], 'contains': ['864.y1', '864.z1', '864.bb1', '864.bg1', '864.bi1', '864.bw1', '864.ce1', '864.fc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 87178291200, 7621226, 36933], 'label': '6912.ia.432.es1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.es1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566710
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hh1', '144.hv1', '216.b1', '216.is1', '216.iu1'], 'contains': ['864.y1', '864.ba1', '864.bb1', '864.bh1', '864.bj1', '864.cd1', '864.cf1', '864.fd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 83468087], 'label': '6912.ia.432.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.et1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566711
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hj1', '144.hw1', '216.d1', '216.it1', '216.iu1', '216.iv1', '216.iw1', '216.ix1', '216.iy1'], 'contains': ['864.y1', '864.bc1', '864.be1', '864.bk1', '864.bm1', '864.cg1', '864.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 36933], 'label': '6912.ia.432.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566712
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hx1', '216.d1', '216.is1', '216.iv1'], 'contains': ['864.y1', '864.bd1', '864.be1', '864.bl1', '864.bn1', '864.ch1', '864.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178291200, 36933, 87100665], 'label': '6912.ia.432.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ev1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566713
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hy1', '216.i1', '216.j1', '216.is1'], 'contains': ['864.z1', '864.ba1', '864.bd1', '864.bx1', '864.ca1', '864.ck1', '864.cs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36239, 87178291200, 36933, 87100665], 'label': '6912.ia.432.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ew1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566714
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hk1', '144.hz1', '216.f1', '216.is1', '216.it1'], 'contains': ['864.z1', '864.bb1', '864.be1', '864.bz1', '864.cb1', '864.cr1', '864.ct1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87178291200, 7621226, 36933, 7629945], 'label': '6912.ia.432.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ex1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566715
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hl1', '144.ia1', '216.j1', '216.it1', '216.iz1', '216.ja1', '216.jb1'], 'contains': ['864.z1', '864.bc1', '864.by1', '864.cc1', '864.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 746], 'label': '6912.ia.432.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ey1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566716
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ib1', '216.f1', '216.is1', '216.iu1'], 'contains': ['864.ba1', '864.bb1', '864.be1', '864.cl1', '864.co1', '864.cv1', '864.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87178291200, 36933, 7629945, 83468087], 'label': '6912.ia.432.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ez1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566717
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1', '8.j1', '12.ds1'], 'contains': ['48.cx1', '48.da1', '48.dc1', '48.du1', '48.dx1', '48.ej1', '48.em1', '72.mb1', '72.ms1'], 'core': '144.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.24.di1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243566718
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ic1', '216.j1', '216.n1', '216.iu1', '216.jc1', '216.jd1', '216.je1', '216.jf1'], 'contains': ['864.ba1', '864.bc1', '864.cm1', '864.cp1', '864.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 87178291200, 36933], 'label': '6912.ia.432.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fa1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566719
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.id1', '216.i1', '216.n1', '216.jg1'], 'contains': ['864.ba1', '864.bd1', '864.cn1', '864.cq1', '864.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 87178291200, 36933, 87100665], 'label': '6912.ia.432.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.t1', 'old_label': '432.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566720
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hm1', '144.ie1', '216.p1', '216.it1', '216.iu1', '216.jh1', '216.ji1', '216.jj1', '216.jk1'], 'contains': ['864.bb1', '864.bc1', '864.cw1', '864.cy1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 36933, 83498639], 'label': '6912.ia.432.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566721
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.if1', '216.p1', '216.is1', '216.jl1'], 'contains': ['864.bb1', '864.bd1', '864.cx1', '864.cz1', '864.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7656719, 87178291200, 36933, 87100665], 'label': '6912.ia.432.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566722
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ig1', '216.y1', '216.z1', '216.iv1', '216.iz1', '216.jc1', '216.jd1', '216.jh1'], 'contains': ['864.bc1', '864.bd1', '864.df1', '864.di1', '864.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87178291200, 36933, 87100665, 87124129], 'label': '6912.ia.432.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fe1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566723
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ho1', '144.ih1', '216.r1', '216.iv1', '216.iy1', '216.ja1', '216.je1', '216.ji1', '216.jj1'], 'contains': ['864.bc1', '864.be1', '864.dh1', '864.dj1', '864.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [32929, 87178291200, 36933, 83480268], 'label': '6912.ia.432.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ff1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566724
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hp1', '144.ii1', '216.u1', '216.iw1', '216.jb1', '216.jc1', '216.ji1'], 'contains': ['864.bc1', '864.dk1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87178291200, 34210, 36933], 'label': '6912.ia.432.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566726
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hq1', '144.ik1', '216.w1', '216.iw1', '216.ix1', '216.ja1', '216.je1', '216.jh1', '216.jk1'], 'contains': ['864.bc1', '864.dn1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178291200, 7654690, 36933], 'label': '6912.ia.432.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566727
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '144.hn1', '144.hr1', '144.hs1', '216.z1', '216.iy1', '216.jb1', '216.jf1', '216.jk1'], 'contains': ['864.b1', '864.bc1', '864.dg1'], 'core': '864.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 36933], 'label': '6912.ia.432.fj1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566728
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.l1', '12.dr1'], 'contains': ['48.d1', '48.ei1', '48.ex1', '72.md1', '72.mw1', '96.bg1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 40280426, 87178291200, 36933, 2676], 'label': '6912.ia.24.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566729
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.il1', '216.r1', '216.iv1', '216.jg1'], 'contains': ['864.bd1', '864.be1', '864.dr1', '864.dt1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7653409, 87178291200, 36933, 87100665], 'label': '6912.ia.432.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566730
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.im1', '216.x1', '216.jg1', '216.jl1'], 'contains': ['864.bd1', '864.du1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 43942690, 36933, 87100665], 'label': '6912.ia.432.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566731
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ht1', '144.in1', '216.y1', '216.jl1'], 'contains': ['864.bd1', '864.ds1', '864.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 87178291200, 36933, 87124129], 'label': '6912.ia.432.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bi1', 'old_label': '432.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566732
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1', '144.v1', '216.hn1', '216.bc1', '216.bd1', '216.be1', '216.bf1'], 'contains': ['864.d1', '864.e1', '864.q1', '864.fe1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218570880, 36933, 87091200], 'label': '6912.ia.432.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566733
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1', '144.x1', '216.b1', '216.bc1', '216.bg1', '216.bh1', '216.bi1', '216.bj1', '216.hs1'], 'contains': ['864.d1', '864.f1', '864.j1', '864.bg1', '864.bh1', '864.ff1', '864.ee1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 36933, 87091200, 83468087], 'label': '6912.ia.432.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566734
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1', '144.z1', '216.c1', '216.bd1', '216.bi1', '216.bk1', '216.bl1', '216.bm1', '216.hs1'], 'contains': ['864.d1', '864.h1', '864.u1', '864.fg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 43909226, 36933, 87091200], 'label': '6912.ia.432.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566735
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ba1', '144.bb1', '144.bc1', '216.b1', '216.bd1', '216.bg1', '216.bk1', '216.bn1', '216.bo1', '216.ht1'], 'contains': ['864.d1', '864.i1', '864.l1', '864.bi1', '864.bj1', '864.fh1', '864.ef1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87261759287, 87091200], 'label': '6912.ia.432.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566736
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bd1', '144.be1', '144.bf1', '216.c1', '216.bc1', '216.bh1', '216.bl1', '216.bn1', '216.bp1', '216.ht1'], 'contains': ['864.d1', '864.k1', '864.x1', '864.fi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87222200426, 36933, 87091200], 'label': '6912.ia.432.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566737
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1', '216.d1', '216.be1', '216.bj1', '216.bm1', '216.bo1', '216.bp1', '216.bq1', '216.br1', '216.bs1', '216.bt1', '216.bu1', '216.bv1', '216.bw1', '216.bx1', '216.hu1'], 'contains': ['864.d1', '864.m1', '864.r1', '864.bk1', '864.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87124129], 'label': '6912.ia.432.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566738
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1', '216.d1', '216.bf1', '216.bg1', '216.bl1', '216.bq1', '216.by1', '216.hv1'], 'contains': ['864.d1', '864.p1', '864.v1', '864.bm1', '864.bn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 87178324129, 36933, 87091200], 'label': '6912.ia.432.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566739
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1', '12.m1', '12.dq1', '12.dr1'], 'contains': ['48.d1', '48.ep1', '48.ey1', '72.me1', '72.nb1', '96.bh1'], 'core': '48.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 7621226, 36933, 2676], 'label': '6912.ia.24.dk1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566740
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bh1', '216.e1', '216.bf1', '216.bi1', '216.bn1', '216.bw1', '216.by1', '216.hu1'], 'contains': ['864.d1', '864.o1', '864.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40297548, 36933], 'label': '6912.ia.432.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566741
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1', '216.e1', '216.be1', '216.bh1', '216.bk1', '216.br1', '216.by1', '216.hv1'], 'contains': ['864.d1', '864.t1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 87218603809, 36933, 87091200], 'label': '6912.ia.432.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.s1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566742
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1', '144.bp1', '216.ho1', '216.bc1', '216.bz1', '216.ca1', '216.cb1', '216.cc1', '216.cd1'], 'contains': ['864.e1', '864.f1', '864.k1', '864.bo1', '864.bq1', '864.fj1', '864.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87305662080, 40280426, 36933, 40279680], 'label': '6912.ia.432.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566743
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bl1', '144.bq1', '216.hn1', '216.bz1', '216.ce1', '216.cf1', '216.cg1'], 'contains': ['864.e1', '864.g1', '864.n1', '864.fk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 43908480, 36933, 87091200], 'label': '6912.ia.432.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566744
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bm1', '144.br1', '216.ho1', '216.bd1', '216.cc1', '216.ce1', '216.ch1', '216.ci1', '216.cj1'], 'contains': ['864.e1', '864.h1', '864.i1', '864.bp1', '864.bq1', '864.fl1', '864.eh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87305662080, 36933, 87096887, 40279680], 'label': '6912.ia.432.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566745
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bn1', '144.bs1', '216.hp1', '216.bc1', '216.ca1', '216.ce1', '216.ch1', '216.ck1', '216.cl1'], 'contains': ['864.e1', '864.j1', '864.x1', '864.fm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 36933, 87091200, 83468087], 'label': '6912.ia.432.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566746
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bo1', '144.bt1', '216.hp1', '216.bd1', '216.bz1', '216.cb1', '216.ci1', '216.ck1', '216.cm1'], 'contains': ['864.e1', '864.l1', '864.u1', '864.fn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 43909226, 36933, 87091200], 'label': '6912.ia.432.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566747
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bu1', '216.hq1', '216.be1', '216.cd1', '216.cf1', '216.cj1', '216.cl1', '216.cm1', '216.ct1', '216.co1', '216.cn1', '216.cp1', '216.cq1', '216.cr1', '216.cs1', '216.cu1'], 'contains': ['864.e1', '864.m1', '864.t1', '864.bs1', '864.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 87218570880, 32929, 36933], 'label': '6912.ia.432.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566748
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bv1', '216.hq1', '216.bf1', '216.cc1', '216.cg1', '216.ck1', '216.ct1', '216.cv1'], 'contains': ['864.e1', '864.p1', '864.o1', '864.bt1', '864.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 87218607813, 36933, 87100665], 'label': '6912.ia.432.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566749
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bx1', '216.hr1', '216.bf1', '216.cb1', '216.cf1', '216.ch1', '216.co1', '216.cv1'], 'contains': ['864.e1', '864.s1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 87218570880, 36933, 87091200], 'label': '6912.ia.432.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566750
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1', '12.ds1'], 'contains': ['48.cy1', '48.cz1', '48.da1', '48.er1', '48.es1', '48.fa1', '48.fb1', '72.mf1', '72.mz1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.24.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243566751
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bw1', '216.hr1', '216.be1', '216.ca1', '216.cg1', '216.ci1', '216.cn1', '216.cv1'], 'contains': ['864.e1', '864.r1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7653409, 87218570880, 36933, 87091200], 'label': '6912.ia.432.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566752
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.by1', '144.cj1', '216.b1', '216.bz1', '216.cw1', '216.cx1', '216.cy1', '216.df1', '216.hw1'], 'contains': ['864.f1', '864.g1', '864.l1', '864.bw1', '864.cd1', '864.fo1', '864.ei1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87261759287, 87091200], 'label': '6912.ia.432.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566753
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bz1', '216.j1', '216.bg1', '216.cc1', '216.cw1', '216.cz1', '216.da1', '216.hx1'], 'contains': ['864.f1', '864.i1', '864.p1', '864.by1', '864.ca1', '864.ck1', '864.cm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 36933, 87178300665, 40279680], 'label': '6912.ia.432.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566754
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ca1', '216.f1', '216.bj1', '216.ca1', '216.cw1', '216.db1', '216.dd1', '216.hy1'], 'contains': ['864.f1', '864.j1', '864.r1', '864.bz1', '864.cl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 83471865, 87091200, 83468087], 'label': '6912.ia.432.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566755
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cb1', '216.i1', '216.bh1', '216.cd1', '216.cx1', '216.db1', '216.dc1', '216.hx1'], 'contains': ['864.f1', '864.k1', '864.t1', '864.ca1', '864.cn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 36933, 87305671545, 40279680], 'label': '6912.ia.432.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566756
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cc1', '216.f1', '216.bg1', '216.cb1', '216.dc1', '216.de1', '216.df1', '216.hz1'], 'contains': ['864.f1', '864.l1', '864.v1', '864.cb1', '864.co1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87261763065, 87261759287, 87091200], 'label': '6912.ia.432.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566757
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cd1', '144.ck1', '216.g1', '216.bz1', '216.cz1', '216.dc1', '216.dd1', '216.dg1', '216.hs1'], 'contains': ['864.f1', '864.n1', '864.u1', '864.fp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 43908480, 36933, 87091200], 'label': '6912.ia.432.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566758
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ce1', '144.cl1', '216.g1', '216.bc1', '216.da1', '216.db1', '216.de1', '216.di1', '216.hw1'], 'contains': ['864.f1', '864.q1', '864.x1', '864.fq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222200426, 87222199680, 36933, 87091200], 'label': '6912.ia.432.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566759
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cf1', '216.h1', '216.bi1', '216.cb1', '216.cx1', '216.da1', '216.dg1', '216.hy1'], 'contains': ['864.f1', '864.s1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 43909226, 36933, 87091200], 'label': '6912.ia.432.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566760
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cg1', '216.h1', '216.bh1', '216.ca1', '216.cy1', '216.cz1', '216.di1', '216.hz1'], 'contains': ['864.f1', '864.w1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 87222200426, 36933, 87091200], 'label': '6912.ia.432.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566761
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1', '8.k1', '12.ds1'], 'contains': ['48.cy1', '48.db1', '48.dc1', '48.eq1', '48.et1', '48.ez1', '48.fc1', '72.mg1', '72.nb1'], 'core': '144.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.24.dm1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243566762
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '216.i1', '216.bi1', '216.cc1', '216.cy1', '216.dd1', '216.de1', '216.ia1'], 'contains': ['864.f1', '864.h1', '864.o1', '864.bx1', '864.cq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40280426, 36933, 87100665], 'label': '6912.ia.432.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566781
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dh1', '216.f1', '216.bg1', '216.ch1', '216.du1', '216.ef1', '216.et1', '216.ie1'], 'contains': ['864.i1', '864.j1', '864.v1', '864.cr1', '864.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87261763065, 87091200, 83468087], 'label': '6912.ia.432.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566763
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ci1', '216.j1', '216.bj1', '216.cd1', '216.df1', '216.dg1', '216.dh1', '216.di1', '216.dk1', '216.dj1', '216.dl1', '216.dm1', '216.dn1', '216.do1', '216.dp1', '216.ia1'], 'contains': ['864.f1', '864.m1', '864.bx1', '864.cc1', '864.cp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 40280426, 36933, 40279680], 'label': '6912.ia.432.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bm1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566764
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cm1', '144.cp1', '216.c1', '216.ce1', '216.cy1', '216.dq1', '216.dr1', '216.ds1', '216.hw1'], 'contains': ['864.g1', '864.h1', '864.x1', '864.fr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 87222200426, 36933, 87091200], 'label': '6912.ia.432.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566765
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cn1', '144.cq1', '216.b1', '216.ce1', '216.cw1', '216.dq1', '216.dt1', '216.du1', '216.ib1'], 'contains': ['864.g1', '864.i1', '864.j1', '864.ce1', '864.cf1', '864.fs1', '864.ej1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87091200, 83468087], 'label': '6912.ia.432.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566766
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.co1', '144.cr1', '216.c1', '216.bz1', '216.cx1', '216.dr1', '216.dt1', '216.dv1', '216.ib1'], 'contains': ['864.g1', '864.k1', '864.u1', '864.ft1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 43909226, 36933, 87091200], 'label': '6912.ia.432.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566767
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cs1', '216.d1', '216.cf1', '216.df1', '216.ds1', '216.du1', '216.dv1', '216.dw1', '216.dx1', '216.dy1', '216.dz1', '216.ea1', '216.eb1', '216.ec1', '216.ed1', '216.ic1'], 'contains': ['864.g1', '864.m1', '864.v1', '864.cg1', '864.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185911680, 32929, 36933, 87124129], 'label': '6912.ia.432.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566768
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '216.d1', '216.cg1', '216.cw1', '216.dr1', '216.dw1', '216.ee1', '216.id1'], 'contains': ['864.g1', '864.p1', '864.r1', '864.ci1', '864.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7653409, 87178324129, 36933, 87091200], 'label': '6912.ia.432.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566769
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ct1', '216.e1', '216.cg1', '216.cy1', '216.dt1', '216.ec1', '216.ee1', '216.ic1'], 'contains': ['864.g1', '864.o1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87185911680, 40297548, 36933], 'label': '6912.ia.432.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566770
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cv1', '216.e1', '216.cf1', '216.cx1', '216.dq1', '216.dx1', '216.ee1', '216.id1'], 'contains': ['864.g1', '864.s1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 87218603809, 36933, 87091200], 'label': '6912.ia.432.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566771
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1', '216.i1', '216.bk1', '216.cj1', '216.dq1', '216.ef1', '216.eg1', '216.hx1'], 'contains': ['864.h1', '864.i1', '864.t1', '864.ck1', '864.cn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87096887, 87305671545, 40279680], 'label': '6912.ia.432.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566772
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1', '8.k1'], 'contains': ['48.dd1', '48.eu1', '48.fd1', '72.mh1', '72.nb1', '96.bj1'], 'core': '144.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 87178291200, 36933, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.24.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dn1', 'old_label': '24.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566773
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cx1', '144.df1', '216.k1', '216.ce1', '216.dd1', '216.ef1', '216.eh1', '216.ej1', '216.hs1'], 'contains': ['864.h1', '864.j1', '864.n1', '864.fu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43908480, 36933, 87091200, 83468087], 'label': '6912.ia.432.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566774
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cy1', '216.l1', '216.bi1', '216.ch1', '216.dq1', '216.ei1', '216.ej1', '216.hy1'], 'contains': ['864.h1', '864.j1', '864.s1', '864.ek1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 36933, 87091200, 83468087], 'label': '6912.ia.432.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bw1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566775
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cz1', '216.n1', '216.bl1', '216.cc1', '216.dr1', '216.eh1', '216.ei1', '216.hx1'], 'contains': ['864.h1', '864.k1', '864.p1', '864.cm1', '864.cn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87096887, 87178300665, 40279680], 'label': '6912.ia.432.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566776
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '144.dg1', '216.k1', '216.bd1', '216.de1', '216.eg1', '216.ei1', '216.ek1', '216.hw1'], 'contains': ['864.h1', '864.l1', '864.q1', '864.fv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222199680, 36933, 87261759287, 87091200], 'label': '6912.ia.432.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.by1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566777
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '216.l1', '216.bk1', '216.ci1', '216.cy1', '216.eh1', '216.ek1', '216.hz1'], 'contains': ['864.h1', '864.l1', '864.w1', '864.el1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 36933, 87261759287, 87091200], 'label': '6912.ia.432.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566778
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '216.m1', '216.bm1', '216.ci1', '216.dd1', '216.dr1', '216.eg1', '216.hy1'], 'contains': ['864.h1', '864.r1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 36933, 83471865, 87091200], 'label': '6912.ia.432.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ca1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566779
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dd1', '216.m1', '216.bl1', '216.ch1', '216.de1', '216.ds1', '216.ef1', '216.hz1'], 'contains': ['864.h1', '864.v1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222200426, 36933, 87261763065, 87091200], 'label': '6912.ia.432.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566780
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.de1', '216.n1', '216.bm1', '216.cj1', '216.ds1', '216.ej1', '216.ek1', '216.el1', '216.en1', '216.em1', '216.eo1', '216.ep1', '216.eq1', '216.er1', '216.es1', '216.ia1'], 'contains': ['864.h1', '864.m1', '864.cp1', '864.cq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87127439, 40279680], 'label': '6912.ia.432.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566892
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kh1', '216.p1', '216.jm1', '216.la1'], 'contains': ['864.br1', '864.bt1', '864.cw1', '864.cz1', '864.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7656719, 36933, 87265419333, 87100665], 'label': '6912.ia.432.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566782
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.di1', '216.f1', '216.bo1', '216.ci1', '216.cw1', '216.eg1', '216.eu1', '216.if1'], 'contains': ['864.i1', '864.l1', '864.r1', '864.ct1', '864.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 83471865, 87261759287, 87091200], 'label': '6912.ia.432.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ce1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566783
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.k1', '3456.m1', '3456.e1', '3456.h1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.e1', '6.b1', '6.m1', '6.s1', '8.c1', '8.j1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 40280426, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.e1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243566784
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.l1', '12.m1', '12.n1', '12.bf1', '12.bg1', '12.bj1', '12.bk1', '18.d1', '18.l1', '24.i1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243566785
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1'], 'contains': ['48.de1', '48.ev1', '48.fe1', '72.mi1', '72.nc1', '96.bj1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178291200, 40297548, 36933, 43548794, 87100665, 83463146], 'label': '6912.ia.24.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '24.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566786
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dj1', '144.dn1', '144.dp1', '216.g1', '216.ce1', '216.cz1', '216.ef1', '216.eu1', '216.ev1', '216.ht1'], 'contains': ['864.i1', '864.n1', '864.x1', '864.fw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43908480, 87222200426, 36933, 87091200], 'label': '6912.ia.432.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566787
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dk1', '144.do1', '216.g1', '216.bd1', '216.da1', '216.eg1', '216.et1', '216.ex1', '216.ib1'], 'contains': ['864.i1', '864.q1', '864.u1', '864.fx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 87222199680, 36933, 87091200], 'label': '6912.ia.432.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566788
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dl1', '216.h1', '216.bn1', '216.ch1', '216.da1', '216.dq1', '216.ev1', '216.if1'], 'contains': ['864.i1', '864.s1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 87222200426, 36933, 87091200], 'label': '6912.ia.432.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ch1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566789
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dm1', '216.h1', '216.bk1', '216.ci1', '216.cz1', '216.dt1', '216.ex1', '216.ie1'], 'contains': ['864.i1', '864.u1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 43909226, 36933, 87091200], 'label': '6912.ia.432.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ci1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566790
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dq1', '216.i1', '216.bn1', '216.cc1', '216.dt1', '216.et1', '216.eu1', '216.ig1'], 'contains': ['864.i1', '864.k1', '864.o1', '864.cs1', '864.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87218571626, 36933, 87100665], 'label': '6912.ia.432.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566791
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dr1', '216.j1', '216.bo1', '216.cj1', '216.du1', '216.ev1', '216.ew1', '216.ex1', '216.ez1', '216.ey1', '216.fa1', '216.fb1', '216.fc1', '216.fd1', '216.fe1', '216.ig1'], 'contains': ['864.i1', '864.m1', '864.cs1', '864.cu1', '864.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218571626, 36933, 40279680], 'label': '6912.ia.432.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ck1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566792
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ds1', '144.dy1', '216.k1', '216.bc1', '216.db1', '216.ei1', '216.et1', '216.ff1', '216.ib1'], 'contains': ['864.j1', '864.k1', '864.q1', '864.fy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222199680, 36933, 87091200, 83468087], 'label': '6912.ia.432.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566793
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dt1', '216.l1', '216.bh1', '216.ca1', '216.dt1', '216.eh1', '216.ff1', '216.ie1'], 'contains': ['864.j1', '864.k1', '864.w1', '864.em1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87298051065, 36933, 87091200, 83468087], 'label': '6912.ia.432.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566794
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.du1', '216.p1', '216.bg1', '216.ck1', '216.cw1', '216.eh1', '216.ei1', '216.ih1'], 'contains': ['864.j1', '864.l1', '864.p1', '864.cw1', '864.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.432.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566795
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dv1', '216.o1', '216.bi1', '216.ck1', '216.dd1', '216.dt1', '216.et1', '216.ii1'], 'contains': ['864.j1', '864.o1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 36933, 87091200], 'label': '6912.ia.432.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.co1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566796
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '12.bn1'], 'contains': ['48.n1', '48.o1', '48.r1', '48.s1', '48.v1', '48.z1', '48.bh1', '48.ge1', '72.bj1', '72.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.24.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566797
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dw1', '216.o1', '216.bh1', '216.cl1', '216.db1', '216.dq1', '216.ef1', '216.ih1'], 'contains': ['864.j1', '864.t1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.432.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cp1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566798
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dx1', '216.p1', '216.bj1', '216.cl1', '216.du1', '216.ej1', '216.ff1', '216.fg1', '216.fi1', '216.fh1', '216.fj1', '216.fk1', '216.fl1', '216.fm1', '216.fn1', '216.ii1'], 'contains': ['864.j1', '864.m1', '864.cy1', '864.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 36933, 87100665], 'label': '6912.ia.432.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cq1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566799
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dz1', '144.eb1', '144.ec1', '216.k1', '216.bz1', '216.dc1', '216.eh1', '216.eu1', '216.fo1', '216.ht1'], 'contains': ['864.k1', '864.l1', '864.n1', '864.fz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43908480, 36933, 87261759287, 87091200], 'label': '6912.ia.432.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566800
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ea1', '216.l1', '216.bn1', '216.cb1', '216.cx1', '216.ei1', '216.fo1', '216.if1'], 'contains': ['864.k1', '864.l1', '864.s1', '864.en1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119759865, 36933, 87261759287, 87091200], 'label': '6912.ia.432.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566801
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ed1', '216.m1', '216.bp1', '216.ca1', '216.db1', '216.dr1', '216.eu1', '216.if1'], 'contains': ['864.k1', '864.r1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222200426, 36933, 83471865, 87091200], 'label': '6912.ia.432.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ct1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566802
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ee1', '216.m1', '216.bl1', '216.cb1', '216.dc1', '216.dv1', '216.et1', '216.ie1'], 'contains': ['864.k1', '864.u1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 36933, 87261763065, 87091200], 'label': '6912.ia.432.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566803
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ef1', '216.n1', '216.bp1', '216.cd1', '216.dv1', '216.ff1', '216.fo1', '216.fp1', '216.fr1', '216.fq1', '216.fs1', '216.ft1', '216.fu1', '216.fv1', '216.fw1', '216.ig1'], 'contains': ['864.k1', '864.m1', '864.db1', '864.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87265418639, 40279680], 'label': '6912.ia.432.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cv1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566804
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eg1', '216.o1', '216.bn1', '216.ck1', '216.cy1', '216.de1', '216.eu1', '216.ij1'], 'contains': ['864.l1', '864.o1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127380345, 87222200426, 36933, 87091200], 'label': '6912.ia.432.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cw1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566805
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eh1', '216.o1', '216.bk1', '216.cm1', '216.cx1', '216.dc1', '216.eg1', '216.ih1'], 'contains': ['864.l1', '864.t1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 36933, 87091200, 87305671545], 'label': '6912.ia.432.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cx1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566806
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ei1', '216.p1', '216.bo1', '216.cm1', '216.df1', '216.ek1', '216.fo1', '216.fx1', '216.fz1', '216.fy1', '216.ga1', '216.gb1', '216.gc1', '216.gd1', '216.ge1', '216.ij1'], 'contains': ['864.l1', '864.m1', '864.dd1', '864.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87185947919, 36933, 87100665], 'label': '6912.ia.432.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cy1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566807
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '12.bn1'], 'contains': ['48.n1', '48.p1', '48.q1', '48.u1', '48.w1', '48.be1', '48.bg1', '48.gf1', '72.bk1', '72.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.24.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566808
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ej1', '216.q1', '216.cf1', '216.dg1', '216.ej1', '216.ev1', '216.fo1', '216.gf1', '216.gg1', '216.gh1', '216.gi1', '216.gj1', '216.gk1', '216.gl1', '216.hh1', '216.hu1'], 'contains': ['864.m1', '864.n1', '864.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 36933, 119750400, 87124129], 'label': '6912.ia.432.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566809
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ek1', '216.z1', '216.bq1', '216.ct1', '216.dh1', '216.dw1', '216.el1', '216.ew1', '216.fg1', '216.fp1', '216.fx1', '216.gf1', '216.gm1', '216.gn1', '216.go1', '216.ik1'], 'contains': ['864.m1', '864.p1', '864.dg1', '864.di1', '864.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 32929, 36933, 87305679948], 'label': '6912.ia.432.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.da1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566810
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.el1', '216.q1', '216.be1', '216.di1', '216.ek1', '216.ex1', '216.ff1', '216.gm1', '216.gp1', '216.gq1', '216.gr1', '216.gs1', '216.gt1', '216.he1', '216.hi1', '216.ic1'], 'contains': ['864.m1', '864.q1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 87124129, 87298041600], 'label': '6912.ia.432.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.db1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566811
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.en1', '216.s1', '216.bw1', '216.co1', '216.dk1', '216.dx1', '216.en1', '216.ez1', '216.fi1', '216.fr1', '216.fz1', '216.gm1', '216.gw1', '216.gx1', '216.hh1', '216.il1'], 'contains': ['864.m1', '864.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43926348, 36933, 87124129], 'label': '6912.ia.432.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dd1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566812
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.em1', '216.r1', '216.bx1', '216.cn1', '216.dj1', '216.dw1', '216.em1', '216.ey1', '216.fh1', '216.fq1', '216.fy1', '216.gl1', '216.gp1', '216.gu1', '216.gv1', '216.il1'], 'contains': ['864.m1', '864.r1', '864.dh1', '864.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 36933, 87124129, 83480268], 'label': '6912.ia.432.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dc1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566813
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eo1', '216.y1', '216.br1', '216.cu1', '216.dl1', '216.dx1', '216.eo1', '216.fa1', '216.fj1', '216.fs1', '216.ga1', '216.gg1', '216.gp1', '216.gy1', '216.gz1', '216.ik1'], 'contains': ['864.m1', '864.t1', '864.di1', '864.ds1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 32929, 36933, 87265400268], 'label': '6912.ia.432.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.de1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566814
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ep1', '216.t1', '216.bm1', '216.cm1', '216.dg1', '216.dv1', '216.ex1', '216.gn1', '216.gw1', '216.gu1', '216.gy1', '216.ha1', '216.hb1', '216.hf1', '216.hj1', '216.ii1'], 'contains': ['864.m1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 36933, 87100665], 'label': '6912.ia.432.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.df1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566815
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eq1', '216.r1', '216.bq1', '216.co1', '216.dm1', '216.ed1', '216.ep1', '216.fb1', '216.fk1', '216.ft1', '216.gb1', '216.gg1', '216.he1', '216.ha1', '216.hc1', '216.im1'], 'contains': ['864.m1', '864.v1', '864.dj1', '864.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 87261771468, 87124129], 'label': '6912.ia.432.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566816
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.er1', '216.s1', '216.br1', '216.cn1', '216.dn1', '216.ec1', '216.eq1', '216.fc1', '216.fl1', '216.fu1', '216.gc1', '216.gf1', '216.hb1', '216.hd1', '216.hi1', '216.im1'], 'contains': ['864.m1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87222217548, 32929, 36933, 87124129], 'label': '6912.ia.432.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dh1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566817
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.es1', '216.t1', '216.bp1', '216.cl1', '216.di1', '216.ds1', '216.ev1', '216.go1', '216.gx1', '216.gv1', '216.gz1', '216.hc1', '216.hd1', '216.hg1', '216.hk1', '216.ij1'], 'contains': ['864.m1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87222200426, 36933, 87100665], 'label': '6912.ia.432.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.di1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566818
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.p1', '12.q1', '12.r1', '12.s1', '12.t1', '12.bx1'], 'contains': ['48.bj1', '48.dh1', '72.cg1', '72.ci1', '72.cj1', '96.g1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.24.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566819
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.et1', '216.u1', '216.bs1', '216.cp1', '216.dp1', '216.dy1', '216.er1', '216.ew1', '216.fh1', '216.fs1', '216.gb1', '216.gh1', '216.gq1', '216.gw1', '216.hd1', '216.in1'], 'contains': ['864.m1', '864.dk1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 19148, 36933, 40279680], 'label': '6912.ia.432.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566820
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eu1', '216.v1', '216.bt1', '216.cq1', '216.do1', '216.dz1', '216.es1', '216.fa1', '216.fi1', '216.fp1', '216.gc1', '216.gi1', '216.gr1', '216.gu1', '216.hc1', '216.in1'], 'contains': ['864.m1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 36933, 40279680], 'label': '6912.ia.432.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566821
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ev1', '216.u1', '216.bu1', '216.cq1', '216.dh1', '216.ea1', '216.eo1', '216.fe1', '216.fk1', '216.fv1', '216.fy1', '216.gj1', '216.gs1', '216.gx1', '216.hb1', '216.io1'], 'contains': ['864.m1', '864.dm1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178310348, 36933, 40279680], 'label': '6912.ia.432.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566822
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ew1', '216.w1', '216.bs1', '216.cr1', '216.dj1', '216.ea1', '216.en1', '216.fb1', '216.fn1', '216.fu1', '216.fx1', '216.gi1', '216.gt1', '216.gz1', '216.hf1', '216.ip1'], 'contains': ['864.m1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87100665, 83481548], 'label': '6912.ia.432.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566823
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ex1', '216.x1', '216.bt1', '216.cs1', '216.dk1', '216.eb1', '216.em1', '216.fc1', '216.fm1', '216.ft1', '216.ga1', '216.gh1', '216.go1', '216.gs1', '216.hj1', '216.ip1'], 'contains': ['864.m1', '864.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87100665, 119769548], 'label': '6912.ia.432.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566824
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ey1', '216.v1', '216.bv1', '216.cp1', '216.dl1', '216.eb1', '216.el1', '216.fd1', '216.fl1', '216.fw1', '216.fz1', '216.gk1', '216.gt1', '216.gv1', '216.ha1', '216.io1'], 'contains': ['864.m1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305681228, 9465, 36933, 40279680], 'label': '6912.ia.432.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.do1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566825
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ez1', '216.w1', '216.bu1', '216.cs1', '216.dm1', '216.dy1', '216.eq1', '216.ey1', '216.fg1', '216.fr1', '216.ge1', '216.gk1', '216.gr1', '216.gy1', '216.hg1', '216.iq1'], 'contains': ['864.m1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87261772748], 'label': '6912.ia.432.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566826
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fa1', '216.x1', '216.bv1', '216.cr1', '216.dn1', '216.dz1', '216.ep1', '216.ez1', '216.fj1', '216.fq1', '216.gd1', '216.gj1', '216.gn1', '216.gq1', '216.hk1', '216.iq1'], 'contains': ['864.m1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87100665, 87298060748], 'label': '6912.ia.432.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566827
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fb1', '216.a1', '216.y1', '216.bw1', '216.ct1', '216.do1', '216.ec1', '216.er1', '216.fd1', '216.fm1', '216.fv1', '216.gd1', '216.gl1', '216.he1', '216.hf1', '216.hg1'], 'contains': ['864.m1', '864.o1', '864.df1', '864.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 127370880, 40312609, 36933], 'label': '6912.ia.432.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dr1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243566828
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fc1', '144.fr1', '144.fs1', '216.a1', '216.z1', '216.bx1', '216.cu1', '216.dp1', '216.ed1', '216.es1', '216.fe1', '216.fn1', '216.fw1', '216.ge1', '216.hh1', '216.hi1', '216.hj1', '216.hk1'], 'contains': ['864.b1', '864.m1', '864.df1'], 'core': '864.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 40297548, 36933, 40279680], 'label': '6912.ia.432.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ds1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566829
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '12.bn1'], 'contains': ['48.s1', '48.t1', '48.w1', '48.x1', '48.y1', '48.bc1', '48.bi1', '48.gg1', '72.ck1', '72.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 43909226, 93405312000, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.24.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566830
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fe1', '216.q1', '216.cg1', '216.cz1', '216.eh1', '216.gf1', '216.hl1', '216.hv1'], 'contains': ['864.n1', '864.p1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43908480, 87178324129, 36933, 87091200], 'label': '6912.ia.432.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.du1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566831
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fd1', '216.ba1', '216.cg1', '216.dd1', '216.eu1', '216.gl1', '216.hl1', '216.hu1'], 'contains': ['864.n1', '864.o1', '864.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40297548, 36933, 119750400], 'label': '6912.ia.432.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566832
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ff1', '216.ba1', '216.cf1', '216.dc1', '216.ef1', '216.gg1', '216.hl1', '216.hv1'], 'contains': ['864.n1', '864.t1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218603809, 43908480, 36933, 87091200], 'label': '6912.ia.432.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566833
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fk1', '216.q1', '216.bf1', '216.da1', '216.ei1', '216.gm1', '216.hm1', '216.id1'], 'contains': ['864.p1', '864.q1', '864.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43941409, 87178324129, 36933, 87091200], 'label': '6912.ia.432.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ea1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566834
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fg1', '216.y1', '216.by1', '216.ct1', '216.ee1', '216.hl1', '216.hm1', '216.ik1'], 'contains': ['864.p1', '864.o1', '864.t1', '864.dq1', '864.ds1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 36933, 87100665, 87305679948], 'label': '6912.ia.432.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566835
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fm1', '216.s1', '216.by1', '216.cv1', '216.ee1', '216.gf1', '216.gm1', '216.ir1'], 'contains': ['864.p1', '864.s1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119768268, 87178324129, 36933, 87091200], 'label': '6912.ia.432.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ec1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566836
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fl1', '216.r1', '216.bq1', '216.cv1', '216.dw1', '216.hl1', '216.hm1', '216.ir1'], 'contains': ['864.p1', '864.r1', '864.v1', '864.dx1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178324129, 36933, 87091200, 83480268], 'label': '6912.ia.432.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566837
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fn1', '216.t1', '216.bl1', '216.ck1', '216.cz1', '216.da1', '216.dr1', '216.ih1'], 'contains': ['864.p1', '864.u1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43909226, 87265391865, 36933, 87091200], 'label': '6912.ia.432.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ed1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566838
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fh1', '216.ba1', '216.bf1', '216.de1', '216.et1', '216.he1', '216.hm1', '216.ic1'], 'contains': ['864.q1', '864.o1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40297548, 36933, 87298041600], 'label': '6912.ia.432.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566839
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fo1', '216.ba1', '216.be1', '216.db1', '216.eg1', '216.gp1', '216.hm1', '216.id1'], 'contains': ['864.q1', '864.r1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7653409, 87218603809, 36933, 87091200], 'label': '6912.ia.432.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ee1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566840
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '12.bn1'], 'contains': ['48.t1', '48.u1', '48.v1', '48.ba1', '48.bb1', '48.bd1', '48.bf1', '48.gh1', '72.cl1', '72.cs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 43908480, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.24.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566841
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fi1', '216.bb1', '216.bw1', '216.cv1', '216.ee1', '216.gl1', '216.hm1', '216.il1'], 'contains': ['864.o1', '864.s1', '864.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 127388748, 40297548, 36933], 'label': '6912.ia.432.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '432.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566842
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fj1', '216.bb1', '216.by1', '216.cv1', '216.ec1', '216.he1', '216.hl1', '216.im1'], 'contains': ['864.o1', '864.v1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 87222232609, 40297548, 36933], 'label': '6912.ia.432.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566843
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fq1', '216.bb1', '216.by1', '216.co1', '216.dx1', '216.gg1', '216.hm1', '216.ir1'], 'contains': ['864.s1', '864.t1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [119768268, 87218603809, 36933, 87091200], 'label': '6912.ia.432.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eg1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566844
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fp1', '216.bb1', '216.br1', '216.cn1', '216.ee1', '216.gp1', '216.hl1', '216.ir1'], 'contains': ['864.r1', '864.t1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218603809, 36933, 87091200, 83480268], 'label': '6912.ia.432.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '432.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ef1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243566845
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.fw1', '144.fx1', '144.fy1', '216.hn1', '216.hs1', '216.ht1', '216.hu1', '216.hv1'], 'contains': ['864.a1', '864.d1', '864.n1', '864.ep1', '864.ga1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 36933, 40279680], 'label': '6912.ia.432.ei1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ei1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566846
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fz1', '144.ga1', '144.gb1', '144.gc1', '216.ho1', '216.hs1', '216.hw1', '216.hx1', '216.hy1', '216.hz1', '216.ia1'], 'contains': ['864.a1', '864.f1', '864.h1', '864.eq1', '864.gb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40280426, 36933, 40279680], 'label': '6912.ia.432.ej1', 'mobius_quo': None, 'mobius_sub': 36, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '432.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ej1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566847
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gd1', '144.ge1', '144.gf1', '144.gg1', '216.hn1', '216.hw1', '216.ib1', '216.ic1', '216.id1'], 'contains': ['864.a1', '864.g1', '864.q1', '864.er1', '864.gc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87185911680, 36933, 40279680], 'label': '6912.ia.432.ek1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ek1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566848
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gh1', '144.gi1', '144.gj1', '144.gk1', '216.ho1', '216.ht1', '216.hx1', '216.ib1', '216.ie1', '216.if1', '216.ig1'], 'contains': ['864.a1', '864.i1', '864.k1', '864.es1', '864.gd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87218571626, 36933, 40279680], 'label': '6912.ia.432.el1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '432.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.el1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566849
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gl1', '144.gm1', '144.gn1', '144.go1', '216.hp1', '216.hs1', '216.hy1', '216.ib1', '216.ie1', '216.ih1', '216.ii1'], 'contains': ['864.a1', '864.j1', '864.u1', '864.et1', '864.ge1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 36933, 40279680], 'label': '6912.ia.432.em1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '432.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.em1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566850
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gp1', '144.gq1', '144.gr1', '144.gs1', '144.gt1', '144.gu1', '144.gv1', '216.hp1', '216.ht1', '216.hw1', '216.hz1', '216.if1', '216.ih1', '216.ij1'], 'contains': ['864.a1', '864.l1', '864.x1', '864.eu1', '864.gf1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127370880, 87222200426, 36933, 40279680], 'label': '6912.ia.432.en1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.en1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566851
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.p1', '12.u1', '12.v1', '12.w1', '12.x1', '12.y1'], 'contains': ['48.bj1', '48.dr1', '72.cm1', '72.di1', '96.h1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.24.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566852
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gw1', '144.ha1', '144.he1', '216.a1', '216.hq1', '216.hu1', '216.ia1', '216.ic1', '216.ig1', '216.ii1', '216.ij1', '216.ik1', '216.il1', '216.im1', '216.in1', '216.io1', '216.ip1', '216.iq1'], 'contains': ['864.a1', '864.m1', '864.o1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 40279680], 'label': '6912.ia.432.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '432.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566853
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gx1', '144.hb1', '216.hq1', '216.hv1', '216.hx1', '216.id1', '216.ih1', '216.ik1', '216.ir1'], 'contains': ['864.a1', '864.p1', '864.t1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 87218603809, 36933, 40279680], 'label': '6912.ia.432.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243566854
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gy1', '144.hc1', '216.hr1', '216.hu1', '216.hy1', '216.id1', '216.if1', '216.il1', '216.ir1'], 'contains': ['864.a1', '864.s1', '864.r1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 36933, 40279680], 'label': '6912.ia.432.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566855
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gz1', '144.hd1', '144.hf1', '216.hr1', '216.hv1', '216.hz1', '216.ic1', '216.ie1', '216.im1', '216.ir1'], 'contains': ['864.a1', '864.v1', '864.w1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 87222232609, 36933, 40279680], 'label': '6912.ia.432.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.er1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243566856
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.io1', '144.iq1', '216.b1', '216.jm1', '216.jn1'], 'contains': ['864.bf1', '864.bg1', '864.bj1', '864.bo1', '864.br1', '864.bw1', '864.cf1', '864.gg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 87265382400], 'label': '6912.ia.432.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566857
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ip1', '144.ir1', '216.b1', '216.jm1', '216.jo1'], 'contains': ['864.bf1', '864.bh1', '864.bi1', '864.bp1', '864.br1', '864.cd1', '864.ce1', '864.gh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 36933, 83468087, 87265382400], 'label': '6912.ia.432.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566858
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.is1', '216.d1', '216.jn1', '216.jo1', '216.jp1', '216.jq1', '216.jr1', '216.js1'], 'contains': ['864.bf1', '864.bk1', '864.bn1', '864.bs1', '864.bv1', '864.cg1', '864.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87265415329], 'label': '6912.ia.432.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566859
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.it1', '216.d1', '216.jm1', '216.jp1'], 'contains': ['864.bf1', '864.bm1', '864.bl1', '864.bt1', '864.bv1', '864.ci1', '864.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87265419333, 87100665], 'label': '6912.ia.432.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566860
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.iu1', '216.is1', '216.bj1', '216.jm1'], 'contains': ['864.bg1', '864.bh1', '864.bl1', '864.bx1', '864.bz1', '864.cl1', '864.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 7656719, 36933, 87100665], 'label': '6912.ia.432.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '432.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566861
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.iv1', '144.jp1', '216.it1', '216.bg1', '216.jm1'], 'contains': ['864.bg1', '864.bi1', '864.bm1', '864.by1', '864.cb1', '864.cr1', '864.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 7621226, 36933, 87178300665], 'label': '6912.ia.432.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566862
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.k1', '12.q1', '12.u1', '12.z1', '12.ba1', '12.bb1'], 'contains': ['48.e1', '48.bj1', '48.ei1', '72.ed1', '72.ee1', '96.i1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.24.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243566863
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.iw1', '216.is1', '216.bg1', '216.jn1'], 'contains': ['864.bg1', '864.bj1', '864.bn1', '864.ca1', '864.cb1', '864.cv1', '864.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 7621226, 87265391865, 36933], 'label': '6912.ia.432.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ft1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566864
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ix1', '144.jq1', '216.it1', '216.bj1', '216.jn1', '216.ju1', '216.jt1', '216.jv1', '216.jw1'], 'contains': ['864.bg1', '864.bk1', '864.bz1', '864.cc1', '864.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 7621226, 36933], 'label': '6912.ia.432.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566865
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.iy1', '216.is1', '216.bg1', '216.jo1'], 'contains': ['864.bh1', '864.bi1', '864.bn1', '864.ck1', '864.co1', '864.cr1', '864.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 87265391865, 36933, 83468087], 'label': '6912.ia.432.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566866
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.iz1', '216.iu1', '216.bg1', '216.jm1'], 'contains': ['864.bh1', '864.bj1', '864.bm1', '864.cm1', '864.co1', '864.cv1', '864.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 36933, 83468087, 87178300665], 'label': '6912.ia.432.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566867
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ja1', '216.iu1', '216.bj1', '216.jo1', '216.jy1', '216.jx1', '216.jz1', '216.ka1'], 'contains': ['864.bh1', '864.bk1', '864.cl1', '864.cp1', '864.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 36933, 83498639], 'label': '6912.ia.432.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566868
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jb1', '216.is1', '216.bo1', '216.jm1'], 'contains': ['864.bi1', '864.bj1', '864.bl1', '864.cs1', '864.ct1', '864.da1', '864.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 87185947919, 36933, 87100665], 'label': '6912.ia.432.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566869
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jc1', '144.jr1', '216.it1', '216.bo1', '216.jo1', '216.kc1', '216.kb1', '216.kd1', '216.ke1'], 'contains': ['864.bi1', '864.bk1', '864.ct1', '864.cu1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87185912426], 'label': '6912.ia.432.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566870
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jd1', '216.iu1', '216.bo1', '216.jn1', '216.kg1', '216.kf1', '216.kh1', '216.ki1'], 'contains': ['864.bj1', '864.bk1', '864.da1', '864.db1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87261789839], 'label': '6912.ia.432.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ga1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566871
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jf1', '144.js1', '216.iy1', '216.bq1', '216.jp1', '216.ju1', '216.jy1', '216.kc1', '216.kg1'], 'contains': ['864.bk1', '864.bm1', '864.dg1', '864.dj1', '864.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87178300665], 'label': '6912.ia.432.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566872
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.je1', '216.iv1', '216.bx1', '216.jp1', '216.jt1', '216.jx1', '216.kb1', '216.kf1'], 'contains': ['864.bk1', '864.bl1', '864.df1', '864.dh1', '864.dr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 36933, 87100665, 87124129], 'label': '6912.ia.432.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566873
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.v1', '12.z1', '12.bc1', '12.bd1', '12.be1', '12.cm1'], 'contains': ['48.bj1', '48.ea1', '72.ef1', '72.et1', '96.j1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87185911680, 36933, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.24.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566874
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jg1', '216.iv1', '216.bq1', '216.js1', '216.jv1', '216.jz1', '216.kd1', '216.kh1'], 'contains': ['864.bk1', '864.bn1', '864.di1', '864.dj1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87265400268], 'label': '6912.ia.432.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566875
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jh1', '144.jt1', '216.iw1', '216.bs1', '216.jq1', '216.jw1', '216.jx1', '216.kc1', '216.kh1'], 'contains': ['864.bk1', '864.dk1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 7654690, 36933], 'label': '6912.ia.432.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ge1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566876
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ji1', '216.ix1', '216.bs1', '216.jr1', '216.jt1', '216.ka1', '216.kd1', '216.kg1'], 'contains': ['864.bk1', '864.dl1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 36933, 83496610], 'label': '6912.ia.432.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566877
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jj1', '144.ju1', '216.iw1', '216.bu1', '216.jr1', '216.ju1', '216.jz1', '216.ke1', '216.kf1'], 'contains': ['864.bk1', '864.dm1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 9465, 36933, 87185945890], 'label': '6912.ia.432.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566878
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jk1', '216.ix1', '216.bu1', '216.jq1', '216.jv1', '216.jy1', '216.kb1', '216.ki1'], 'contains': ['864.bk1', '864.do1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87261787810, 9465, 36933], 'label': '6912.ia.432.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566879
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jl1', '144.jn1', '144.jo1', '144.jv1', '216.iy1', '216.bx1', '216.js1', '216.jw1', '216.ka1', '216.ke1', '216.ki1'], 'contains': ['864.b1', '864.bk1', '864.dh1'], 'core': '864.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933], 'label': '6912.ia.432.gi1', 'mobius_quo': None, 'mobius_sub': 36, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '432.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566880
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jm1', '216.iv1', '216.bq1', '216.jp1'], 'contains': ['864.bm1', '864.bl1', '864.bn1', '864.dq1', '864.dx1', '864.dt1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 36933, 87100665, 87265415329], 'label': '6912.ia.432.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '432.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566881
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jx1', '216.j1', '216.cc1', '216.jm1'], 'contains': ['864.bo1', '864.bp1', '864.bt1', '864.bx1', '864.by1', '864.cm1', '864.cs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36239, 36933, 87265419333, 87100665], 'label': '6912.ia.432.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '432.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566882
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jy1', '216.i1', '216.cc1', '216.cd1'], 'contains': ['864.bo1', '864.bq1', '864.bu1', '864.bx1', '864.ca1', '864.cn1', '864.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36239, 87305662080, 36933, 87100665], 'label': '6912.ia.432.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ex1', 'old_label': '432.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566883
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jz1', '216.f1', '216.jm1', '216.jn1'], 'contains': ['864.bo1', '864.br1', '864.bv1', '864.bz1', '864.cb1', '864.cv1', '864.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7621226, 36933, 7629945, 87265382400], 'label': '6912.ia.432.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566884
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.l1', '12.r1', '12.w1', '12.bc1', '12.bf1', '12.bg1'], 'contains': ['48.bj1', '48.ei1', '72.fi1', '72.fj1', '96.k1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.24.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566885
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ka1', '216.j1', '216.cd1', '216.jn1', '216.kj1', '216.kk1', '216.kl1', '216.km1'], 'contains': ['864.bo1', '864.bs1', '864.ca1', '864.cc1', '864.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 36933, 746], 'label': '6912.ia.432.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566886
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kb1', '216.f1', '216.jm1', '216.jo1'], 'contains': ['864.bp1', '864.br1', '864.bv1', '864.cl1', '864.co1', '864.cr1', '864.ct1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 7629945, 83468087, 87265382400], 'label': '6912.ia.432.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.go1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566887
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kc1', '216.i1', '216.cc1', '216.cj1'], 'contains': ['864.bp1', '864.bq1', '864.bu1', '864.ck1', '864.cn1', '864.cq1', '864.cs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87305662080, 40280426, 36933, 87100665], 'label': '6912.ia.432.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ex1', 'old_label': '432.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566888
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kd1', '216.j1', '216.cj1', '216.jo1', '216.kn1', '216.ko1', '216.kp1', '216.kq1'], 'contains': ['864.bp1', '864.bs1', '864.ck1', '864.cp1', '864.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 40280426, 36933], 'label': '6912.ia.432.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566889
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ke1', '216.n1', '216.cd1', '216.cj1', '216.kr1', '216.ks1', '216.kt1', '216.ku1'], 'contains': ['864.bq1', '864.bs1', '864.cn1', '864.cp1', '864.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87218570880, 36933, 87127439], 'label': '6912.ia.432.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gr1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566890
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kf1', '216.n1', '216.cc1', '216.kv1'], 'contains': ['864.bq1', '864.bt1', '864.cm1', '864.cq1', '864.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 36933, 87265419333, 87100665], 'label': '6912.ia.432.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.t1', 'old_label': '432.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gs1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566891
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kg1', '216.p1', '216.jn1', '216.jo1', '216.kw1', '216.kx1', '216.ky1', '216.kz1'], 'contains': ['864.br1', '864.bs1', '864.cx1', '864.cy1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87265419333, 83498639], 'label': '6912.ia.432.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gt1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566893
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ki1', '216.z1', '216.ct1', '216.jp1', '216.kj1', '216.kn1', '216.kr1', '216.kw1'], 'contains': ['864.bs1', '864.bt1', '864.dg1', '864.df1', '864.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36933, 87100665, 87124129, 87265382400], 'label': '6912.ia.432.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566894
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kj1', '216.y1', '216.ct1', '216.cu1', '216.kk1', '216.ko1', '216.ks1', '216.kt1'], 'contains': ['864.bs1', '864.bu1', '864.df1', '864.di1', '864.ds1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87305662080, 36933, 87100665, 87124129], 'label': '6912.ia.432.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566895
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.j1', '12.n1', '12.p1', '12.v1', '12.bx1', '12.cm1', '18.y1', '18.bl1', '24.be1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.o1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243566896
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.k1', '12.s1', '12.w1', '12.bd1', '12.bh1', '12.bi1'], 'contains': ['48.f1', '48.bj1', '48.ex1', '72.fv1', '72.fw1', '72.fx1', '96.l1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 87218571626, 36933, 2676, 40279680], 'label': '6912.ia.24.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243566897
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kk1', '216.r1', '216.jp1', '216.js1', '216.kl1', '216.kp1', '216.kx1', '216.ky1'], 'contains': ['864.bs1', '864.bv1', '864.dh1', '864.dj1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [32929, 36933, 83480268, 87265415329], 'label': '6912.ia.432.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566898
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kl1', '216.u1', '216.cp1', '216.jq1', '216.km1', '216.kn1', '216.ks1', '216.kx1'], 'contains': ['864.bs1', '864.dk1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 34210, 36933], 'label': '6912.ia.432.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gy1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566899
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.km1', '216.u1', '216.cq1', '216.jr1', '216.kj1', '216.kq1', '216.kt1', '216.ky1'], 'contains': ['864.bs1', '864.dl1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218570880, 40313890, 36933], 'label': '6912.ia.432.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566900
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kn1', '216.v1', '216.cp1', '216.cq1', '216.kk1', '216.ko1', '216.kr1', '216.ku1'], 'contains': ['864.bs1', '864.dl1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 127405090, 87218570880, 36933], 'label': '6912.ia.432.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ha1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566901
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ko1', '216.w1', '216.jq1', '216.jr1', '216.kl1', '216.kp1', '216.kw1', '216.kz1'], 'contains': ['864.bs1', '864.dn1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7654690, 36933, 87265419333], 'label': '6912.ia.432.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566902
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jw1', '144.kp1', '216.z1', '216.cu1', '216.js1', '216.km1', '216.kq1', '216.ku1', '216.kz1'], 'contains': ['864.b1', '864.bs1', '864.di1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218570880, 32929, 36933], 'label': '6912.ia.432.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566903
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kq1', '216.r1', '216.jp1', '216.kv1'], 'contains': ['864.bt1', '864.bv1', '864.dx1', '864.dr1', '864.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7653409, 36933, 87265419333, 87100665], 'label': '6912.ia.432.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '432.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566904
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kr1', '216.x1', '216.kv1', '216.la1'], 'contains': ['864.bt1', '864.du1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43942690, 36933, 87265419333, 87100665], 'label': '6912.ia.432.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.he1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566905
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ks1', '216.y1', '216.ct1', '216.la1'], 'contains': ['864.bt1', '864.bu1', '864.dq1', '864.ds1', '864.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 87305662080, 36933, 87124129], 'label': '6912.ia.432.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.w1', 'old_label': '432.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hf1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566906
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kt1', '216.is1', '216.df1', '216.jm1'], 'contains': ['864.bw1', '864.bx1', '864.cb1', '864.cd1', '864.ch1', '864.co1', '864.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185947919, 87185911680, 36933, 87100665], 'label': '6912.ia.432.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566907
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.q1', '12.x1', '12.bd1', '12.bf1', '12.bj1', '12.cz1'], 'contains': ['48.bj1', '48.ep1', '72.gg1', '72.gh1', '96.m1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.24.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566908
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ku1', '144.kv1', '216.it1', '216.cw1', '216.jm1'], 'contains': ['864.bw1', '864.by1', '864.bz1', '864.ce1', '864.ci1', '864.ct1', '864.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7621226, 36933, 7629945, 87178300665], 'label': '6912.ia.432.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566909
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kw1', '216.is1', '216.cw1', '216.jn1'], 'contains': ['864.bw1', '864.bz1', '864.ca1', '864.cf1', '864.cj1', '864.cx1', '864.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7621226, 87265391865, 36933, 7629945], 'label': '6912.ia.432.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566910
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.kx1', '144.ky1', '144.kz1', '216.it1', '216.df1', '216.jn1', '216.lc1', '216.lb1', '216.ld1', '216.le1'], 'contains': ['864.bw1', '864.cb1', '864.cc1', '864.cg1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87185912426], 'label': '6912.ia.432.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566911
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lb1', '144.lg1', '216.jb1', '216.dh1', '216.ju1', '216.kj1', '216.lc1'], 'contains': ['864.cc1', '864.dg1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87178324129, 36933, 746], 'label': '6912.ia.432.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hl1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566912
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.la1', '216.iz1', '216.do1', '216.dp1', '216.jt1', '216.kj1', '216.kk1', '216.lb1'], 'contains': ['864.cc1', '864.df1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 36933, 746], 'label': '6912.ia.432.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566913
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lc1', '144.lh1', '216.ja1', '216.dj1', '216.jt1', '216.jw1', '216.kl1', '216.lc1', '216.ld1'], 'contains': ['864.cc1', '864.dh1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 36933, 83495329, 83496610], 'label': '6912.ia.432.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hm1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566914
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ld1', '216.iz1', '216.dh1', '216.dl1', '216.jv1', '216.kk1', '216.km1', '216.ld1'], 'contains': ['864.cc1', '864.di1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218603809, 36933, 746], 'label': '6912.ia.432.hn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566915
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.le1', '144.li1', '144.lk1', '216.ja1', '216.dm1', '216.ju1', '216.jv1', '216.kl1', '216.lb1', '216.le1'], 'contains': ['864.cc1', '864.dj1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87261787810, 9465, 36933, 87261786529], 'label': '6912.ia.432.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ho1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566916
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '144.lf1', '144.lj1', '144.ll1', '216.jb1', '216.dp1', '216.jw1', '216.km1', '216.le1'], 'contains': ['864.b1', '864.cc1', '864.dk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 36933, 746], 'label': '6912.ia.432.hp1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '432.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566917
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ln1', '216.is1', '216.cw1', '216.jo1'], 'contains': ['864.cd1', '864.ce1', '864.cj1', '864.ck1', '864.cl1', '864.ct1', '864.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87265391865, 36933, 7629945, 83468087], 'label': '6912.ia.432.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.hq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566918
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.l1', '12.t1', '12.u1', '12.be1', '12.bj1', '12.bk1'], 'contains': ['48.bj1', '48.ex1', '72.gq1', '72.gr1', '72.gs1', '96.n1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87305681228, 40312609, 93405312000, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.24.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566919
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lo1', '216.iu1', '216.cw1', '216.jm1'], 'contains': ['864.cd1', '864.cf1', '864.ci1', '864.cl1', '864.cm1', '864.cw1', '864.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 7629945, 83468087, 87178300665], 'label': '6912.ia.432.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.hr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566920
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lp1', '216.iu1', '216.df1', '216.jo1', '216.lg1', '216.lf1', '216.lh1', '216.li1'], 'contains': ['864.cd1', '864.cg1', '864.co1', '864.cp1', '864.dd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87261789839], 'label': '6912.ia.432.hs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hs1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566921
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lr1', '216.is1', '216.du1', '216.jm1'], 'contains': ['864.ce1', '864.cf1', '864.ch1', '864.cr1', '864.cs1', '864.cv1', '864.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7656719, 87185911680, 36933, 87100665], 'label': '6912.ia.432.ht1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '432.ht1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ht1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566922
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lq1', '144.ls1', '216.it1', '216.du1', '216.jo1', '216.lk1', '216.lj1', '216.ll1', '216.lm1'], 'contains': ['864.ce1', '864.cg1', '864.cr1', '864.cu1', '864.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 7621226, 36933], 'label': '6912.ia.432.hu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566923
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lt1', '216.iu1', '216.du1', '216.jn1', '216.lo1', '216.ln1', '216.lp1', '216.lq1'], 'contains': ['864.cf1', '864.cg1', '864.cv1', '864.cy1', '864.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 83498639], 'label': '6912.ia.432.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566924
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lv1', '144.md1', '216.iy1', '216.dw1', '216.jp1', '216.lc1', '216.lg1', '216.lk1', '216.lo1'], 'contains': ['864.cg1', '864.ci1', '864.dg1', '864.dh1', '864.dx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [32929, 36933, 83480268, 87178300665], 'label': '6912.ia.432.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566925
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lu1', '216.iv1', '216.ed1', '216.jp1', '216.lb1', '216.lf1', '216.lj1', '216.ln1'], 'contains': ['864.cg1', '864.ch1', '864.df1', '864.dj1', '864.dt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87100665, 87124129], 'label': '6912.ia.432.hw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566926
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lw1', '216.iv1', '216.dw1', '216.js1', '216.ld1', '216.lh1', '216.ll1', '216.lp1'], 'contains': ['864.cg1', '864.cj1', '864.dh1', '864.di1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [32929, 36933, 87265400268, 83480268], 'label': '6912.ia.432.hy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hy1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566927
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lx1', '144.me1', '144.mh1', '216.iw1', '216.dy1', '216.jq1', '216.le1', '216.lf1', '216.lk1', '216.lp1'], 'contains': ['864.cg1', '864.dk1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 87185945890], 'label': '6912.ia.432.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.hz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566928
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ly1', '216.ix1', '216.dy1', '216.jr1', '216.lb1', '216.li1', '216.ll1', '216.lo1'], 'contains': ['864.cg1', '864.dl1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87261787810, 9465, 87185911680, 36933], 'label': '6912.ia.432.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ia1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ia1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566929
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.s1', '12.y1', '12.z1', '12.bg1', '12.bk1', '12.df1'], 'contains': ['48.bj1', '48.ey1', '72.ha1', '72.hb1', '72.hc1', '96.o1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87185912426, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.24.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566930
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lz1', '144.mf1', '216.iw1', '216.ea1', '216.jr1', '216.lc1', '216.lh1', '216.lm1', '216.ln1'], 'contains': ['864.cg1', '864.dm1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 7654690, 36933], 'label': '6912.ia.432.ib1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ib1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ib1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566931
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ma1', '216.ix1', '216.ea1', '216.jq1', '216.ld1', '216.lg1', '216.lj1', '216.lq1'], 'contains': ['864.cg1', '864.dn1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87185911680, 36933, 83496610], 'label': '6912.ia.432.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ic1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ic1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566932
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lm1', '144.mb1', '144.mg1', '144.mi1', '216.iy1', '216.ed1', '216.js1', '216.le1', '216.li1', '216.lm1', '216.lq1'], 'contains': ['864.b1', '864.cg1', '864.dj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 87185911680, 32929, 36933], 'label': '6912.ia.432.id1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.id1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.id1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243566933
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mc1', '216.iv1', '216.dw1', '216.jp1'], 'contains': ['864.ci1', '864.ch1', '864.cj1', '864.dq1', '864.dx1', '864.dr1', '864.dy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7653409, 36933, 87100665, 87265415329], 'label': '6912.ia.432.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '432.ie1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ie1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566934
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ml1', '216.jf1', '216.dh1', '216.el1', '216.jy1', '216.kn1', '216.kr1', '216.lg1'], 'contains': ['864.cp1', '864.dg1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 40280426, 87178324129, 36933], 'label': '6912.ia.432.ih1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.if1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ih1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566935
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mj1', '216.jc1', '216.dp1', '216.er1', '216.jx1', '216.kn1', '216.ks1', '216.lf1'], 'contains': ['864.cp1', '864.df1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 36933, 127371626], 'label': '6912.ia.432.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.ig1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.if1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566936
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mk1', '216.jd1', '216.do1', '216.er1', '216.es1', '216.ko1', '216.kr1', '216.kt1'], 'contains': ['864.cp1', '864.df1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 40280426, 36933], 'label': '6912.ia.432.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '432.ih1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ig1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566937
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mm1', '216.je1', '216.dj1', '216.jx1', '216.ka1', '216.kp1', '216.lg1', '216.lh1'], 'contains': ['864.cp1', '864.dh1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 7654690, 36933, 83495329], 'label': '6912.ia.432.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.ii1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ii1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566938
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mn1', '216.jc1', '216.dh1', '216.eo1', '216.jz1', '216.kq1', '216.kt1', '216.lh1'], 'contains': ['864.cp1', '864.di1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218603809, 40280426, 36933], 'label': '6912.ia.432.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.ij1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ij1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566939
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mo1', '216.jd1', '216.dl1', '216.el1', '216.eo1', '216.ko1', '216.ks1', '216.ku1'], 'contains': ['864.cp1', '864.di1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87218603809, 36933, 87127439], 'label': '6912.ia.432.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.ik1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ik1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566940
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.v1', '12.ba1', '12.bf1', '12.bh1', '12.bk1', '12.bx1'], 'contains': ['48.bj1', '72.if1', '72.il1', '72.ip1', '96.p1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.24.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566941
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mp1', '216.je1', '216.dm1', '216.jy1', '216.jz1', '216.kp1', '216.lf1', '216.li1'], 'contains': ['864.cp1', '864.dj1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87185945890, 87261786529], 'label': '6912.ia.432.il1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.il1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.il1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566942
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mq1', '144.mt1', '216.jf1', '216.dp1', '216.es1', '216.ka1', '216.kq1', '216.ku1', '216.li1'], 'contains': ['864.b1', '864.cp1', '864.dl1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 32929, 40280426, 36933], 'label': '6912.ia.432.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '432.im1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.im1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566943
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mr1', '216.jg1', '216.em1', '216.kv1'], 'contains': ['864.cq1', '864.dr1', '864.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 43942690, 36933, 87100665], 'label': '6912.ia.432.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '432.in1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.in1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566944
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ms1', '216.jg1', '216.ep1', '216.kv1'], 'contains': ['864.cq1', '864.dt1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185944609, 36933, 87222233890, 87100665], 'label': '6912.ia.432.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1', 'old_label': '432.io1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.io1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566945
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mu1', '144.mz1', '216.jb1', '216.ew1', '216.kc1', '216.kn1', '216.lk1'], 'contains': ['864.cu1', '864.dg1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87178324129, 34210, 36933], 'label': '6912.ia.432.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.ip1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566946
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.my1', '216.iz1', '216.fd1', '216.fe1', '216.kb1', '216.kn1', '216.ko1', '216.lj1'], 'contains': ['864.cu1', '864.df1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 36933, 87178291946], 'label': '6912.ia.432.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.iq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ip1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566947
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mv1', '144.na1', '216.ja1', '216.ey1', '216.kb1', '216.ke1', '216.kp1', '216.lk1', '216.ll1'], 'contains': ['864.cu1', '864.dh1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87261787810, 9465, 36933, 83495329], 'label': '6912.ia.432.ir1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ir1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ir1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566948
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nb1', '216.iz1', '216.ew1', '216.fa1', '216.kd1', '216.ko1', '216.kq1', '216.ll1'], 'contains': ['864.cu1', '864.di1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218603809, 40313890, 36933], 'label': '6912.ia.432.is1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.is1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.is1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566949
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mw1', '144.nc1', '216.ja1', '216.fb1', '216.kc1', '216.kd1', '216.kp1', '216.lj1', '216.lm1'], 'contains': ['864.cu1', '864.dj1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83496610, 87261786529], 'label': '6912.ia.432.it1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.it1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.it1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566950
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mx1', '144.nd1', '144.ne1', '144.nf1', '216.jb1', '216.fe1', '216.ke1', '216.kq1', '216.lm1'], 'contains': ['864.b1', '864.cu1', '864.dm1'], 'core': '864.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 32929, 36933, 87178291946], 'label': '6912.ia.432.iu1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.iu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566951
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.p1', '12.bb1', '12.bg1', '12.bi1', '12.bj1', '12.cm1'], 'contains': ['48.bj1', '72.ig1', '72.im1', '96.q1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 87222199680, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.24.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566952
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nh1', '144.nr1', '216.jk1', '216.fg1', '216.ju1', '216.jy1', '216.kw1', '216.lk1', '216.lo1'], 'contains': ['864.cy1', '864.dg1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 36933, 83498639], 'label': '6912.ia.432.iw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.iv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566953
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ng1', '216.jh1', '216.fn1', '216.jt1', '216.jx1', '216.kw1', '216.lj1', '216.ln1'], 'contains': ['864.cy1', '864.df1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 83463146, 87124129, 87109068], 'label': '6912.ia.432.iv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.iw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566954
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ni1', '144.ns1', '216.ji1', '216.fh1', '216.jw1', '216.jx1', '216.kx1', '216.lk1', '216.lp1'], 'contains': ['864.cy1', '864.dh1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 36933, 83498639, 83495329], 'label': '6912.ia.432.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.ix1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ix1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566955
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nj1', '216.jj1', '216.fh1', '216.jt1', '216.ka1', '216.ky1', '216.ll1', '216.lo1'], 'contains': ['864.cy1', '864.dh1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 7621226, 36933, 83495329], 'label': '6912.ia.432.iy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.iy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iy1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566956
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nk1', '216.jh1', '216.fg1', '216.jv1', '216.jz1', '216.kz1', '216.ll1', '216.lp1'], 'contains': ['864.cy1', '864.di1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83498639, 87265415329], 'label': '6912.ia.432.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.iz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566957
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nl1', '144.nt1', '216.ji1', '216.fk1', '216.ju1', '216.jz1', '216.ky1', '216.lm1', '216.ln1'], 'contains': ['864.cy1', '864.dj1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83498639, 87261786529], 'label': '6912.ia.432.ja1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ja1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ja1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566958
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nm1', '216.jj1', '216.fk1', '216.jv1', '216.jy1', '216.kx1', '216.lj1', '216.lq1'], 'contains': ['864.cy1', '864.dj1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7621226, 36933, 87261786529], 'label': '6912.ia.432.jb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jb1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566959
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nn1', '144.nq1', '144.nu1', '144.nv1', '216.jk1', '216.fn1', '216.jw1', '216.ka1', '216.kz1', '216.lm1', '216.lq1'], 'contains': ['864.b1', '864.cy1', '864.dn1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 32929, 7621226, 36933], 'label': '6912.ia.432.jc1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '432.jc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566960
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.no1', '216.jl1', '216.fj1', '216.la1'], 'contains': ['864.cz1', '864.ds1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7656719, 36933, 87305695009, 87100665], 'label': '6912.ia.432.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.u1', 'old_label': '432.jd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566961
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.np1', '144.nw1', '216.jl1', '216.fm1', '216.la1'], 'contains': ['864.cz1', '864.du1', '864.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40297548, 36933, 87100665, 83463146], 'label': '6912.ia.432.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '432.je1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.je1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566962
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.r1', '12.y1', '12.ba1', '12.be1', '12.bi1', '12.cz1'], 'contains': ['48.bj1', '72.ih1', '72.in1', '96.r1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.24.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243566963
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nz1', '216.jf1', '216.ew1', '216.fp1', '216.kg1', '216.kj1', '216.kr1', '216.lo1'], 'contains': ['864.db1', '864.dg1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87178324129, 40313890, 36933], 'label': '6912.ia.432.jh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.jf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566964
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nx1', '216.jc1', '216.fe1', '216.fv1', '216.kf1', '216.kj1', '216.kt1', '216.ln1'], 'contains': ['864.db1', '864.df1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 9465, 87305662826, 36933], 'label': '6912.ia.432.jf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.jg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jf1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566965
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ny1', '216.jd1', '216.fd1', '216.fv1', '216.fw1', '216.kk1', '216.kr1', '216.ks1'], 'contains': ['864.db1', '864.df1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127388748, 9465, 87218571626, 36933], 'label': '6912.ia.432.jg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.jh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jg1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566966
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oa1', '216.je1', '216.ey1', '216.kf1', '216.ki1', '216.kl1', '216.lo1', '216.lp1'], 'contains': ['864.db1', '864.dh1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87185945890, 83495329], 'label': '6912.ia.432.ji1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ji1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ji1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566967
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ob1', '216.jc1', '216.ew1', '216.fs1', '216.kh1', '216.km1', '216.ks1', '216.lp1'], 'contains': ['864.db1', '864.di1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218603809, 34210, 36933], 'label': '6912.ia.432.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.jj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566968
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oc1', '216.jd1', '216.fa1', '216.fp1', '216.fs1', '216.kk1', '216.kt1', '216.ku1'], 'contains': ['864.db1', '864.di1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 127405090, 87218603809, 36933], 'label': '6912.ia.432.jk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '432.jk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jk1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566969
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.od1', '216.je1', '216.fb1', '216.kg1', '216.kh1', '216.kl1', '216.ln1', '216.lq1'], 'contains': ['864.db1', '864.dj1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7654690, 36933, 87261786529], 'label': '6912.ia.432.jl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jl1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566970
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oe1', '144.oh1', '144.oi1', '216.jf1', '216.fe1', '216.fw1', '216.ki1', '216.km1', '216.ku1', '216.lq1'], 'contains': ['864.b1', '864.db1', '864.do1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 32929, 87218571626, 36933], 'label': '6912.ia.432.jm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.jm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jm1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566971
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.of1', '216.jg1', '216.fq1', '216.kv1'], 'contains': ['864.dc1', '864.dr1', '864.dv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7653409, 36933, 87222233890, 87100665], 'label': '6912.ia.432.jn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1', 'old_label': '432.jn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jn1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566972
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.og1', '216.jg1', '216.ft1', '216.kv1'], 'contains': ['864.dc1', '864.dt1', '864.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185944609, 43942690, 36933, 87100665], 'label': '6912.ia.432.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.o1', 'old_label': '432.jo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jo1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566973
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.t1', '12.x1', '12.bb1', '12.bc1', '12.bh1', '12.df1'], 'contains': ['48.bj1', '72.ii1', '72.io1', '72.iq1', '96.s1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.24.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243566974
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ok1', '144.ou1', '216.jk1', '216.fx1', '216.kc1', '216.kg1', '216.kw1', '216.lc1', '216.lg1'], 'contains': ['864.dd1', '864.dg1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 87178324129, 7654690, 36933], 'label': '6912.ia.432.jq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566975
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oj1', '216.jh1', '216.ge1', '216.kb1', '216.kf1', '216.kw1', '216.lb1', '216.lf1'], 'contains': ['864.dd1', '864.df1', '864.dp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87124129, 87109068, 87261754346], 'label': '6912.ia.432.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566976
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ol1', '144.ov1', '216.ji1', '216.fy1', '216.ke1', '216.kf1', '216.ky1', '216.lc1', '216.lh1'], 'contains': ['864.dd1', '864.dh1', '864.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 83495329, 87261789839], 'label': '6912.ia.432.jr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jr1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566977
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.om1', '216.jj1', '216.fy1', '216.kb1', '216.ki1', '216.kx1', '216.ld1', '216.lg1'], 'contains': ['864.dd1', '864.dh1', '864.do1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87185912426, 83495329], 'label': '6912.ia.432.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.js1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.js1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566978
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.on1', '216.jh1', '216.fx1', '216.kd1', '216.kh1', '216.kz1', '216.ld1', '216.lh1'], 'contains': ['864.dd1', '864.di1', '864.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 7654690, 36933, 87265415329], 'label': '6912.ia.432.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jt1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566979
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oo1', '144.ow1', '144.oz1', '216.ji1', '216.gb1', '216.kc1', '216.kh1', '216.kx1', '216.le1', '216.lf1'], 'contains': ['864.dd1', '864.dj1', '864.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87261789839, 87261786529], 'label': '6912.ia.432.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.ju1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ju1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566980
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.op1', '216.jj1', '216.gb1', '216.kd1', '216.kg1', '216.ky1', '216.lb1', '216.li1'], 'contains': ['864.dd1', '864.dj1', '864.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87185912426, 87261786529], 'label': '6912.ia.432.jv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jv1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566981
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oq1', '144.ot1', '144.ox1', '144.oy1', '144.pa1', '144.pb1', '144.pd1', '216.jk1', '216.ge1', '216.ke1', '216.ki1', '216.kz1', '216.le1', '216.li1'], 'contains': ['864.b1', '864.dd1', '864.dp1'], 'core': '864.b1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 32929, 36933, 87185912426], 'label': '6912.ia.432.jw1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '432.jw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jw1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566982
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.or1', '216.jl1', '216.ga1', '216.la1'], 'contains': ['864.de1', '864.ds1', '864.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [43942690, 36933, 87305695009, 87100665], 'label': '6912.ia.432.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.u1', 'old_label': '432.jx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jx1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566983
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.os1', '144.pc1', '144.pe1', '216.jl1', '216.gd1', '216.la1'], 'contains': ['864.de1', '864.dv1', '864.dw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40297548, 36933, 87100665, 87261754346], 'label': '6912.ia.432.jy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.u1', 'old_label': '432.jy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jy1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243566984
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.x1', '8.e1', '12.bn1'], 'contains': ['48.o1', '48.p1', '48.y1', '48.bd1', '48.bn1', '48.br1', '48.cb1', '48.fn1', '48.gi1', '72.jf1', '72.jg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.24.bm1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243566985
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.pi1', '144.pl1', '216.hn1', '216.lr1'], 'contains': ['864.eo1', '864.ev1', '864.ez1', '864.ep1', '864.er1', '864.fe1', '864.fk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 40316613, 87178291200, 127407813], 'label': '6912.ia.432.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.jz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566986
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pj1', '144.pm1', '216.ho1', '216.lr1'], 'contains': ['864.eo1', '864.ew1', '864.ex1', '864.ea1', '864.eb1', '864.eq1', '864.es1', '864.fj1', '864.fl1', '864.eg1', '864.eh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 127370880, 40280426, 87178328133], 'label': '6912.ia.432.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ka1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566987
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pk1', '144.pn1', '216.hp1', '216.lr1'], 'contains': ['864.eo1', '864.ey1', '864.fa1', '864.et1', '864.eu1', '864.fm1', '864.fn1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87178291200, 43944719, 127407813], 'label': '6912.ia.432.kd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566988
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.px1', '144.qi1', '216.b1', '216.lr1', '216.ls1'], 'contains': ['864.ev1', '864.ew1', '864.ey1', '864.fc1', '864.fd1', '864.ff1', '864.fh1', '864.fo1', '864.fs1', '864.gg1', '864.gh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7657413, 87178328133, 87091200, 83468087], 'label': '6912.ia.432.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ki1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243566989
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.py1', '144.qj1', '216.c1', '216.lr1', '216.ls1'], 'contains': ['864.ev1', '864.ex1', '864.fa1', '864.fg1', '864.fi1', '864.fr1', '864.ft1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7657413, 43944719, 87178328133, 87091200], 'label': '6912.ia.432.kj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566990
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.pz1', '144.qk1', '216.g1', '216.lr1', '216.ls1'], 'contains': ['864.ew1', '864.ez1', '864.fa1', '864.fp1', '864.fq1', '864.fw1', '864.fx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [43945413, 43944719, 87178328133, 87091200], 'label': '6912.ia.432.kk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ke1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567086
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.cd1', '192.ce1', '288.cl1', '288.jt1', '288.hu1', '288.jz1', '288.ka1'], 'contains': ['1152.b1', '1152.r1', '1152.bc1', '1728.bg1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 87178328133], 'label': '6912.ia.576.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.cp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566991
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qa1', '144.ql1', '216.k1', '216.lr1', '216.ls1'], 'contains': ['864.ex1', '864.ey1', '864.ez1', '864.fu1', '864.fv1', '864.fy1', '864.fz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [43945413, 83476887, 87178328133, 87091200], 'label': '6912.ia.432.kl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566992
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qb1', '144.qc1', '144.qm1', '216.hn1', '216.ls1'], 'contains': ['864.ev1', '864.ez1', '864.fb1', '864.fe1', '864.fk1', '864.ga1', '864.gc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 127370880, 87178328133, 40279680], 'label': '6912.ia.432.km1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.kg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.km1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566993
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qd1', '144.qe1', '144.qn1', '216.ho1', '216.ls1'], 'contains': ['864.ew1', '864.ex1', '864.fb1', '864.fj1', '864.fl1', '864.gb1', '864.gd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [127370880, 40280426, 87178328133, 40279680], 'label': '6912.ia.432.kn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '432.kh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243566994
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qf1', '144.qg1', '144.qh1', '144.qo1', '216.hp1', '216.ls1'], 'contains': ['864.ey1', '864.fa1', '864.fb1', '864.fm1', '864.fn1', '864.ge1', '864.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [127370880, 43944719, 87178328133, 40279680], 'label': '6912.ia.432.ko1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ki1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ko1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566995
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1', '8.f1', '12.bn1'], 'contains': ['48.q1', '48.r1', '48.bf1', '48.bi1', '48.bn1', '48.ca1', '48.cf1', '48.fo1', '48.gj1', '72.jh1', '72.ji1', '72.jj1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.24.bn1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243566996
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pf1', '144.pg1', '216.b1'], 'contains': ['864.dz1', '864.ea1', '864.ec1', '864.fc1', '864.fd1', '864.ee1', '864.ef1', '864.ei1', '864.ej1', '864.gg1', '864.gh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7620480, 87178291200, 87128133, 83468087], 'label': '6912.ia.432.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '432.kj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243566997
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ph1', '216.l1'], 'contains': ['864.eb1', '864.ec1', '864.ed1', '864.ek1', '864.el1', '864.em1', '864.en1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [119759865, 87128133, 83476887, 87178328133], 'label': '6912.ia.432.ka1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.l1', 'old_label': '432.kk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ka1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566998
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.po1', '144.pp1', '216.hs1', '216.lr1'], 'contains': ['864.ep1', '864.eq1', '864.et1', '864.ff1', '864.fg1', '864.fp1', '864.fu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 40316613, 43944719, 127407813], 'label': '6912.ia.432.ke1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '432.kl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ke1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243566999
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pq1', '144.pr1', '144.ps1', '216.ht1', '216.lr1'], 'contains': ['864.ep1', '864.es1', '864.eu1', '864.fh1', '864.fi1', '864.fw1', '864.fz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 7657413, 87222235919, 127407813], 'label': '6912.ia.432.kf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.km1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567000
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pt1', '144.pu1', '216.hw1', '216.lr1'], 'contains': ['864.eq1', '864.er1', '864.eu1', '864.fo1', '864.fq1', '864.fr1', '864.fv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87185948613, 87222235919, 127407813], 'label': '6912.ia.432.kg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567001
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.pv1', '144.pw1', '216.ib1', '216.lr1'], 'contains': ['864.er1', '864.es1', '864.et1', '864.fs1', '864.ft1', '864.fx1', '864.fy1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87185948613, 43944719, 127407813], 'label': '6912.ia.432.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ko1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567002
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qp1', '144.qr1', '216.bc1', '216.lr1', '216.ls1'], 'contains': ['864.fe1', '864.ff1', '864.fi1', '864.fj1', '864.fm1', '864.fq1', '864.fy1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87218607813, 7657413, 83476887, 87091200], 'label': '6912.ia.432.kp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567003
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qq1', '144.qs1', '216.bd1', '216.lr1', '216.ls1'], 'contains': ['864.fe1', '864.fg1', '864.fh1', '864.fl1', '864.fn1', '864.fv1', '864.fx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7620480, 87218607813, 43944719, 87091200], 'label': '6912.ia.432.kq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567004
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qt1', '144.qv1', '216.bz1', '216.lr1', '216.ls1'], 'contains': ['864.fj1', '864.fk1', '864.fn1', '864.fo1', '864.fp1', '864.ft1', '864.fz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87218607813, 43945413, 43944719, 87091200], 'label': '6912.ia.432.kr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567005
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qu1', '144.qw1', '216.ce1', '216.lr1', '216.ls1'], 'contains': ['864.fk1', '864.fl1', '864.fm1', '864.fr1', '864.fs1', '864.fu1', '864.fw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87218607813, 43945413, 83476887, 87091200], 'label': '6912.ia.432.ks1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ks1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ks1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567006
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.bo1', '12.bp1', '12.bq1', '12.br1', '12.bs1', '12.by1', '12.bz1', '12.ca1', '12.cf1', '12.cg1', '12.cp1', '18.z1', '18.bj1', '24.de1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 127380345, 7620480], 'label': '6912.ia.6.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567007
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '12.bo1', '12.by1', '12.bz1'], 'contains': ['48.b1', '48.bq1', '48.cc1', '48.gk1', '72.jf1', '72.jm1', '96.br1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.bo1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567008
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qx1', '144.qy1', '144.rc1', '216.hs1', '216.ls1'], 'contains': ['864.ff1', '864.fg1', '864.fp1', '864.fu1', '864.ga1', '864.gb1', '864.ge1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 40279680], 'label': '6912.ia.432.kt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '432.kt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567009
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qz1', '144.ra1', '144.rb1', '144.rd1', '216.ht1', '216.ls1'], 'contains': ['864.fh1', '864.fi1', '864.fw1', '864.fz1', '864.ga1', '864.gd1', '864.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [127370880, 7657413, 87222200426, 40279680], 'label': '6912.ia.432.ku1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.ku1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ku1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567010
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.re1', '144.rf1', '144.rg1', '144.rh1', '216.hw1', '216.ls1'], 'contains': ['864.fo1', '864.fq1', '864.fr1', '864.fv1', '864.gb1', '864.gc1', '864.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [127370880, 87222200426, 87185948613, 40279680], 'label': '6912.ia.432.kv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567011
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '432.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ri1', '144.rj1', '144.rk1', '216.ib1', '216.ls1'], 'contains': ['864.fs1', '864.ft1', '864.fx1', '864.fy1', '864.gc1', '864.gd1', '864.ge1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [127370880, 43909226, 87185948613, 40279680], 'label': '6912.ia.432.kw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '432.kw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567012
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.d1', '192.e1', '192.f1', '288.h1', '288.cl1', '288.cm1', '288.cn1', '288.co1', '288.cp1', '288.cq1', '288.cr1'], 'contains': ['1152.a1', '1152.b1', '1728.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933], 'label': '6912.ia.576.a1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '576.a1', 'normal_contained_in': ['144.a1', '144.c1'], 'normal_contains': ['1152.a1', '1152.b1'], 'normalizer': '1.a1', 'old_label': '576.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567013
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1', 'complements': ['12.dp1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '192.cy1', '192.cz1', '288.a1', '288.e1', '288.lx1', '288.ma1', '288.mf1', '288.mj1', '288.mm1', '288.mq1'], 'contains': ['1152.o1', '1728.a1'], 'core': '576.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 40279680], 'label': '6912.ia.576.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '576.b1', 'normal_contained_in': ['192.a1', '288.a1', '288.e1'], 'normal_contains': ['1728.a1', '2304.a1'], 'normalizer': '1.a1', 'old_label': '576.b1', 'projective_image': '6912.ia', 'quotient_action_image': '12.4', 'quotient_action_kernel': '48.29', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '576.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567014
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': ['12.dr1', '12.du1', '12.dt1', '12.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '192.da1', '192.dc1', '288.b1', '288.f1', '288.jo1', '288.mb1', '288.mg1', '288.mi1', '288.mo1', '288.ms1'], 'contains': ['1728.a1', '2304.c1'], 'core': '576.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 47537280, 40279680], 'label': '6912.ia.576.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '576.c1', 'normal_contained_in': ['192.a1', '288.b1', '288.f1'], 'normal_contains': ['1728.a1'], 'normalizer': '1.a1', 'old_label': '576.c1', 'projective_image': '6912.ia', 'quotient_action_image': '4.2', 'quotient_action_kernel': '144.128', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '576.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567015
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hn1', '192.c1', '192.d1', '288.g1', '288.cb1', '288.ce1', '288.cf1', '288.cg1'], 'contains': ['1152.c1', '1152.l1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87178291200, 36933, 2676], 'label': '6912.ia.576.g1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '576.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567016
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.db1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fu1', '192.c1', '192.e1', '288.cc1', '288.cd1', '288.ch1', '288.cj1', '288.ck1'], 'contains': ['1152.d1', '1152.m1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87178291200, 47537280, 36933], 'label': '6912.ia.576.h1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '576.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567017
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fv1', '144.hs1', '144.ht1', '192.c1', '192.f1', '288.ci1'], 'contains': ['1152.g1', '1152.n1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120116474, 87178291200, 36933], 'label': '6912.ia.576.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bb1', 'old_label': '576.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567018
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '8.e1', '12.bl1'], 'contains': ['48.bo1', '48.bs1', '48.ce1', '48.gl1', '72.jg1', '72.jm1', '96.bs1'], 'core': '144.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.24.bp1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '24.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567019
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1', '288.a1', '288.h1', '288.i1', '288.m1', '288.n1', '288.q1', '288.r1', '288.t1', '288.w1', '288.y1', '288.bb1', '288.be1', '288.bf1', '288.bh1', '288.bi1', '288.bg1', '288.bk1', '288.bj1', '288.bl1', '288.bm1', '288.bn1', '288.bo1', '288.bp1'], 'contains': ['1152.a1', '1152.o1', '1152.i1', '1728.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 36933, 40279680], 'label': '6912.ia.576.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567020
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fr1', '192.b1', '288.g1', '288.j1', '288.l1', '288.o1', '288.p1', '288.s1', '288.u1', '288.x1', '288.z1', '288.bc1', '288.bq1', '288.br1', '288.bs1', '288.bt1', '288.bw1'], 'contains': ['1152.c1', '1152.p1', '1152.j1', '1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [36933, 2676, 40279680], 'label': '6912.ia.576.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567021
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fs1', '192.b1', '288.k1', '288.v1', '288.ba1', '288.bd1', '288.bu1', '288.bv1', '288.bx1'], 'contains': ['1152.e1', '1152.q1', '1152.k1', '1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36933, 93405314676, 40279680], 'label': '6912.ia.576.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '576.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567022
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.g1', '192.h1', '288.cl1', '288.i1', '288.ct1', '288.cu1', '288.cw1', '288.cy1', '288.db1', '288.de1', '288.dg1', '288.df1', '288.dh1'], 'contains': ['1152.a1', '1152.r1', '1728.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 93405312000, 36933], 'label': '6912.ia.576.j1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567023
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jn1', '192.g1', '192.i1', '288.cb1', '288.j1', '288.cs1', '288.cv1', '288.cx1', '288.cz1', '288.dc1'], 'contains': ['1152.c1', '1152.s1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 36933, 2676], 'label': '6912.ia.576.k1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567024
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jo1', '192.g1', '192.j1', '288.k1', '288.da1', '288.dd1'], 'contains': ['1152.e1', '1152.t1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 36933, 93405314676], 'label': '6912.ia.576.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '576.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567025
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '192.h1', '192.i1', '192.j1', '288.cc1', '288.di1', '288.dj1', '288.dk1', '288.dl1'], 'contains': ['1152.d1', '1152.u1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 47537280, 36933], 'label': '6912.ia.576.m1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '576.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567026
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ir1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.jw1', '192.k1', '288.g1', '288.l1', '288.cs1', '288.dm1', '288.dn1', '288.do1', '288.dp1'], 'contains': ['1152.c1', '1152.v1', '1728.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218570880, 36933, 2676], 'label': '6912.ia.576.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567027
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.k1', '288.h1', '288.m1', '288.ct1', '288.dq1', '288.dr1', '288.ds1', '288.dt1', '288.du1', '288.dv1', '288.dw1', '288.dx1'], 'contains': ['1152.a1', '1152.w1', '1728.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87218570880, 93405312000, 36933], 'label': '6912.ia.576.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567028
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.l1', '192.m1', '288.cm1', '288.n1', '288.cu1', '288.dq1', '288.dy1', '288.eb1', '288.ed1', '288.ee1', '288.eg1', '288.eh1', '288.ek1'], 'contains': ['1152.a1', '1152.x1', '1728.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 36933, 746], 'label': '6912.ia.576.p1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '576.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567029
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '12.bo1', '12.by1', '12.ca1'], 'contains': ['48.b1', '48.bx1', '48.cg1', '48.gm1', '72.jh1', '72.jn1', '96.bt1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.bq1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567030
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ga1', '192.l1', '192.n1', '288.cd1', '288.di1', '288.dz1', '288.ec1', '288.ef1', '288.ei1', '288.el1'], 'contains': ['1152.d1', '1152.y1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [47537280, 36933, 746], 'label': '6912.ia.576.q1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '576.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567031
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gb1', '192.l1', '192.o1', '288.ea1', '288.ej1', '288.em1'], 'contains': ['1152.f1', '1152.z1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [93452849280, 36933, 746], 'label': '6912.ia.576.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.dt1', 'old_label': '576.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567032
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '192.m1', '192.n1', '192.o1', '288.ce1', '288.o1', '288.cv1', '288.dm1', '288.en1'], 'contains': ['1152.c1', '1152.ba1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [36933, 746, 2676], 'label': '6912.ia.576.s1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '576.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567033
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.lm1', '192.p1', '192.q1', '192.r1', '288.cb1', '288.p1', '288.cs1', '288.en1', '288.eo1', '288.ep1', '288.eq1'], 'contains': ['1152.c1', '1152.bb1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185911680, 36933, 2676], 'label': '6912.ia.576.t1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567034
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.p1', '192.s1', '288.cl1', '288.q1', '288.ct1', '288.dy1', '288.er1', '288.et1', '288.eu1', '288.ev1', '288.ex1', '288.ew1', '288.ey1'], 'contains': ['1152.a1', '1152.bc1', '1728.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87185911680, 93405312000, 36933], 'label': '6912.ia.576.u1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567035
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gf1', '192.q1', '192.s1', '288.cc1', '288.dz1', '288.es1', '288.ez1', '288.fa1'], 'contains': ['1152.d1', '1152.bd1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 47537280, 36933], 'label': '6912.ia.576.v1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '576.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567036
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gg1', '192.r1', '192.s1', '288.ea1', '288.fb1'], 'contains': ['1152.f1', '1152.be1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87185911680, 93452849280, 36933], 'label': '6912.ia.576.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '576.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567037
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.t1', '288.cn1', '288.n1', '288.r1', '288.cw1', '288.dr1', '288.ds1', '288.eb1', '288.er1', '288.fc1', '288.fd1', '288.fe1', '288.ff1', '288.fg1', '288.fh1', '288.fi1'], 'contains': ['1152.a1', '1152.bf1', '1728.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 40280426, 36933], 'label': '6912.ia.576.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '576.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567038
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.mt1', '192.t1', '288.cf1', '288.o1', '288.s1', '288.cx1', '288.dn1', '288.do1', '288.eo1'], 'contains': ['1152.c1', '1152.bg1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40280426, 36933, 2676], 'label': '6912.ia.576.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567039
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gh1', '192.u1', '192.v1', '192.w1', '288.cd1', '288.dj1', '288.ec1', '288.es1', '288.fj1', '288.fk1', '288.fl1'], 'contains': ['1152.d1', '1152.bh1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [47537280, 36933, 87178291946], 'label': '6912.ia.576.z1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '576.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567040
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1', '8.f1', '12.bl1'], 'contains': ['48.bo1', '48.by1', '48.ci1', '48.gn1', '72.ji1', '72.jn1', '96.bu1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 40279680, 87222200426, 127370880, 7620480], 'label': '6912.ia.24.br1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567041
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.u1', '192.x1', '288.cm1', '288.t1', '288.cy1', '288.dr1', '288.ed1', '288.et1', '288.fc1', '288.fm1', '288.fn1', '288.fo1', '288.fp1'], 'contains': ['1152.a1', '1152.bi1', '1728.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 36933, 87178291946], 'label': '6912.ia.576.ba1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '576.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567042
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ne1', '192.v1', '192.x1', '288.ce1', '288.u1', '288.cz1', '288.dn1', '288.ep1'], 'contains': ['1152.c1', '1152.bj1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [36933, 2676, 87178291946], 'label': '6912.ia.576.bb1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '576.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567043
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nf1', '192.w1', '192.x1', '288.v1', '288.da1'], 'contains': ['1152.e1', '1152.bk1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36933, 93405314676, 87178291946], 'label': '6912.ia.576.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '576.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567044
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.y1', '192.z1', '192.ba1', '288.co1', '288.w1', '288.cu1', '288.cw1', '288.dt1', '288.ee1', '288.et1', '288.eu1', '288.fd1', '288.fm1', '288.fq1', '288.fr1', '288.fs1', '288.ft1', '288.fu1'], 'contains': ['1152.a1', '1152.bl1', '1728.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 83468087], 'label': '6912.ia.576.bd1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '576.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567045
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.nq1', '192.y1', '192.bb1', '288.cg1', '288.x1', '288.cv1', '288.cx1', '288.dp1', '288.ep1', '288.eq1'], 'contains': ['1152.c1', '1152.bm1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6851, 36933, 83468087], 'label': '6912.ia.576.be1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567046
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gn1', '192.z1', '192.bb1', '288.ch1', '288.di1', '288.ef1', '288.es1', '288.fj1', '288.fv1', '288.fw1'], 'contains': ['1152.d1', '1152.bn1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79833600, 36933, 83468087], 'label': '6912.ia.576.bf1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '576.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567047
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.go1', '144.nv1', '144.nw1', '192.ba1', '192.bb1', '288.ci1'], 'contains': ['1152.g1', '1152.bo1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [43561327, 36933, 83468087], 'label': '6912.ia.576.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '576.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567048
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bc1', '288.cn1', '288.t1', '288.y1', '288.db1', '288.dq1', '288.ds1', '288.eg1', '288.eu1', '288.fe1', '288.ff1', '288.fn1', '288.fq1', '288.fx1', '288.fy1', '288.fz1'], 'contains': ['1152.a1', '1152.bp1', '1728.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87218571626, 36933], 'label': '6912.ia.576.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '576.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567049
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oh1', '192.bc1', '288.cf1', '288.u1', '288.z1', '288.dc1', '288.dm1', '288.do1', '288.eq1'], 'contains': ['1152.c1', '1152.bq1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218571626, 36933, 2676], 'label': '6912.ia.576.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567050
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oi1', '192.bc1', '288.v1', '288.ba1', '288.dd1'], 'contains': ['1152.e1', '1152.br1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218571626, 36933, 93405314676], 'label': '6912.ia.576.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567051
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.be1', '8.f1'], 'contains': ['48.bp1', '48.bz1', '48.ck1', '48.go1', '72.jj1', '72.jn1', '96.bv1'], 'core': '144.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36933, 47537280, 40279680, 87222200426, 127370880, 93525427956, 7620480], 'label': '6912.ia.24.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '24.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567052
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bd1', '192.be1', '192.bf1', '288.co1', '288.bb1', '288.cy1', '288.db1', '288.dt1', '288.dy1', '288.eh1', '288.er1', '288.fg1', '288.fo1', '288.fr1', '288.fs1', '288.fx1', '288.ga1', '288.gb1'], 'contains': ['1152.a1', '1152.bs1', '1728.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 36933, 87261759287], 'label': '6912.ia.576.bk1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '576.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567053
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ot1', '192.bd1', '192.bg1', '192.bh1', '288.cg1', '288.bc1', '288.cz1', '288.dc1', '288.dp1', '288.en1', '288.eo1'], 'contains': ['1152.c1', '1152.bt1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6851, 36933, 87261759287], 'label': '6912.ia.576.bl1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567054
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gr1', '192.be1', '192.bg1', '192.bi1', '288.ch1', '288.dj1', '288.dz1', '288.ei1', '288.fk1', '288.fv1', '288.gc1'], 'contains': ['1152.d1', '1152.bu1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [79833600, 36933, 87261759287], 'label': '6912.ia.576.bm1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.lx1', 'old_label': '576.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567055
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.oy1', '192.bd1', '192.bi1', '192.bj1', '288.bd1', '288.da1', '288.dd1'], 'contains': ['1152.e1', '1152.bv1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405318851, 36933, 87261759287], 'label': '6912.ia.576.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '576.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567056
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gt1', '192.be1', '192.bh1', '192.bj1', '288.ea1', '288.ej1', '288.gd1'], 'contains': ['1152.f1', '1152.bw1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93485145600, 36933, 87261759287], 'label': '6912.ia.576.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.kz1', 'old_label': '576.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567057
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gu1', '144.pb1', '144.pc1', '192.bf1', '192.bg1', '192.bj1', '288.ci1'], 'contains': ['1152.g1', '1152.bx1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [43561327, 36933, 87261759287], 'label': '6912.ia.576.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ci1', 'old_label': '576.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567058
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gv1', '144.pd1', '144.pe1', '192.bf1', '192.bh1', '192.bi1', '192.bj1'], 'contains': ['1152.h1', '1152.by1', '1728.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [93448873327, 36933, 87261759287], 'label': '6912.ia.576.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '576.bq1', 'old_label': '576.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567059
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bk1', '288.c1', '288.cp1', '288.be1', '288.de1', '288.du1', '288.ek1', '288.ev1', '288.fh1', '288.fp1', '288.ft1', '288.fy1', '288.ga1', '288.gf1', '288.ge1', '288.gg1', '288.gh1', '288.gi1', '288.gj1', '288.gk1', '288.gl1', '288.gm1', '288.gn1', '288.go1'], 'contains': ['1152.a1', '1728.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 32929, 36933], 'label': '6912.ia.576.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '576.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567060
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bl1', '288.cp1', '288.bh1', '288.dg1', '288.dv1', '288.ed1', '288.ex1', '288.fe1', '288.fr1', '288.gf1', '288.gp1', '288.gw1'], 'contains': ['1152.a1', '1728.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 87178324129, 36933], 'label': '6912.ia.576.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '576.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567061
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cq1', '288.be1', '288.bg1', '288.df1', '288.dv1', '288.dw1', '288.eb1', '288.ew1', '288.fi1', '288.fn1', '288.fu1', '288.fz1', '288.gb1', '288.ge1', '288.gp1', '288.gq1', '288.gr1', '288.gs1', '288.gt1', '288.gu1', '288.gv1'], 'contains': ['1152.a1', '1728.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 127403809, 36933], 'label': '6912.ia.576.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '576.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567062
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.bp1', '12.bz1', '12.ca1', '12.cb1', '12.cc1', '12.cd1'], 'contains': ['48.b1', '48.cm1', '48.co1', '72.jk1', '72.jo1', '96.bw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567063
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bm1', '288.cr1', '288.bj1', '288.de1', '288.df1', '288.dx1', '288.ee1', '288.ex1', '288.ey1', '288.fd1', '288.fo1', '288.fx1', '288.gg1', '288.gw1', '288.gq1', '288.gx1'], 'contains': ['1152.a1', '1728.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 83495329], 'label': '6912.ia.576.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '576.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567064
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cq1', '288.bh1', '288.bl1', '288.dh1', '288.du1', '288.dw1', '288.eg1', '288.ey1', '288.fc1', '288.ff1', '288.fs1', '288.gh1', '288.gp1', '288.gr1', '288.gx1'], 'contains': ['1152.a1', '1728.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 36933, 87265415329], 'label': '6912.ia.576.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '576.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567065
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bn1', '288.cr1', '288.bn1', '288.dg1', '288.dh1', '288.dx1', '288.eh1', '288.ev1', '288.ew1', '288.fg1', '288.fm1', '288.fq1', '288.gi1', '288.gw1', '288.gs1', '288.gx1'], 'contains': ['1152.a1', '1728.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 36933, 87261786529], 'label': '6912.ia.576.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '576.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567066
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ha1', '192.bk1', '288.cj1', '288.dk1', '288.el1', '288.ez1', '288.fl1', '288.fw1', '288.gc1', '288.gy1', '288.gz1', '288.ha1', '288.hb1', '288.hc1', '288.hd1', '288.he1', '288.hf1'], 'contains': ['1152.d1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [32929, 47537280, 36933], 'label': '6912.ia.576.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '576.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567067
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.hp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hb1', '192.bl1', '288.cj1', '288.dl1', '288.ec1', '288.fa1', '288.fv1', '288.gy1', '288.hg1'], 'contains': ['1152.d1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178324129, 47537280, 36933], 'label': '6912.ia.576.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '576.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567068
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hc1', '192.bm1', '288.ck1', '288.dk1', '288.ef1', '288.fa1', '288.fk1', '288.gz1', '288.hg1'], 'contains': ['1152.d1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79833600, 36933, 83495329], 'label': '6912.ia.576.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '576.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567069
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hd1', '192.bn1', '288.ck1', '288.dl1', '288.ei1', '288.ez1', '288.fj1', '288.ha1', '288.hg1'], 'contains': ['1152.d1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [79833600, 36933, 87261786529], 'label': '6912.ia.576.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '576.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567070
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.he1', '192.bk1', '288.em1', '288.fb1', '288.gd1', '288.hi1', '288.hj1', '288.hk1', '288.hl1'], 'contains': ['1152.f1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [32929, 93452849280, 36933], 'label': '6912.ia.576.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '576.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567071
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hf1', '192.bn1', '288.ej1', '288.fb1', '288.hi1'], 'contains': ['1152.f1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93485145600, 36933, 87261786529], 'label': '6912.ia.576.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.pn1', 'old_label': '576.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567072
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ir1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cc1', '288.g1', '288.iq1', '288.jh1', '288.ji1', '288.jj1', '288.jk1', '288.jl1', '288.jm1', '288.jn1'], 'contains': ['1152.l1', '1152.p1', '1152.v1', '1728.bf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178328133, 2676, 40279680], 'label': '6912.ia.576.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.cd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567073
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '12.by1', '12.cb1'], 'contains': ['48.b1', '48.cn1', '48.cp1', '72.jl1', '72.jp1', '96.bx1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 87218603809, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567074
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ir1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.bo1', '288.g1', '288.iq1', '288.hq1', '288.hr1', '288.hs1', '288.ht1'], 'contains': ['1152.l1', '1152.j1', '1152.v1', '1728.s1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 87178291200, 2676], 'label': '6912.ia.576.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.ce1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567075
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.bz1', '192.cd1', '288.cb1', '288.jh1', '288.hq1', '288.jq1', '288.jr1'], 'contains': ['1152.l1', '1152.s1', '1152.bb1', '1728.bg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87178328133, 2676], 'label': '6912.ia.576.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.cf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567076
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qc1', '192.bz1', '192.ce1', '288.cc1', '288.js1'], 'contains': ['1152.m1', '1152.u1', '1152.bd1', '1728.bg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 47537280, 87178328133], 'label': '6912.ia.576.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '576.cg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.di1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567077
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qd1', '192.ca1', '192.cf1', '288.cd1', '288.js1'], 'contains': ['1152.m1', '1152.y1', '1152.bh1', '1728.bh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [36239, 47537280, 87178328133], 'label': '6912.ia.576.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '576.ch1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567078
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.ca1', '192.cg1', '288.ce1', '288.ji1', '288.hr1', '288.jq1'], 'contains': ['1152.l1', '1152.ba1', '1152.bj1', '1728.bh1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [746, 87178328133, 2676], 'label': '6912.ia.576.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '576.ci1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567079
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.ch1', '288.cf1', '288.ji1', '288.jj1', '288.hr1', '288.hs1', '288.jr1'], 'contains': ['1152.l1', '1152.bg1', '1152.bq1', '1728.bi1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40280426, 87178328133, 2676], 'label': '6912.ia.576.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.cj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567080
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.cb1', '192.ci1', '288.cg1', '288.jk1', '288.ht1', '288.jq1', '288.jr1'], 'contains': ['1152.l1', '1152.bm1', '1152.bt1', '1728.bj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6851, 87178328133, 83468087], 'label': '6912.ia.576.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.ck1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567081
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.qg1', '192.cb1', '192.cj1', '288.ch1', '288.js1'], 'contains': ['1152.m1', '1152.bn1', '1152.bu1', '1728.bj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [79833600, 83476887, 87178328133], 'label': '6912.ia.576.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '576.cl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567082
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.qh1', '192.cb1', '192.ck1', '288.ci1'], 'contains': ['1152.n1', '1152.bo1', '1152.bx1', '1728.bj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': None, 'generators': [43561327, 83476887, 87178328133], 'label': '6912.ia.576.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ci1', 'old_label': '576.cm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567083
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cc1', '288.e1', '288.h1', '288.ir1', '288.jt1', '288.ju1', '288.jv1', '288.jw1', '288.jx1', '288.jy1'], 'contains': ['1152.b1', '1152.o1', '1152.w1', '1728.bf1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87178328133, 40279680], 'label': '6912.ia.576.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.cn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567084
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '12.bo1', '12.cf1', '12.cg1'], 'contains': ['48.c1', '48.bq1', '48.cg1', '48.gp1', '72.jq1', '72.jr1', '72.js1', '96.cc1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.bv1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567085
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.bo1', '288.h1', '288.ir1', '288.hu1', '288.hv1', '288.hw1', '288.hx1', '288.hy1'], 'contains': ['1152.b1', '1152.i1', '1152.w1', '1728.s1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40316613, 93405312000, 87178291200], 'label': '6912.ia.576.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.co1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567127
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cu1', '288.bu1', '288.iu1', '288.lr1', '288.lw1', '288.lz1'], 'contains': ['1152.q1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [43945413, 93405314676, 87091200], 'label': '6912.ia.576.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '576.ea1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ey1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567087
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cf1', '192.cg1', '288.cm1', '288.ju1', '288.hv1', '288.jz1'], 'contains': ['1152.b1', '1152.x1', '1152.bi1', '1728.bh1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [36239, 93405312000, 87178328133], 'label': '6912.ia.576.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '576.cq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567088
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ch1', '288.cn1', '288.ju1', '288.jv1', '288.hv1', '288.hw1', '288.ka1'], 'contains': ['1152.b1', '1152.bf1', '1152.bp1', '1728.bi1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87178328133, 40315919], 'label': '6912.ia.576.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.cr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ds1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567089
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ci1', '192.cj1', '192.ck1', '288.co1', '288.jw1', '288.hx1', '288.jz1', '288.ka1'], 'contains': ['1152.b1', '1152.bl1', '1152.bs1', '1728.bj1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 83476887, 87178328133], 'label': '6912.ia.576.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.cs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567090
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.by1', '288.a1', '288.ir1', '288.is1', '288.iv1', '288.iy1', '288.iz1', '288.jc1', '288.je1'], 'contains': ['1152.o1', '1152.i1', '1728.be1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000], 'label': '6912.ia.576.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.ct1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567091
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.by1', '288.bw1', '288.iq1', '288.it1', '288.iw1', '288.ix1', '288.ja1', '288.jd1', '288.jf1'], 'contains': ['1152.p1', '1152.j1', '1728.be1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40316613, 127370880, 2676], 'label': '6912.ia.576.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.cu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.de1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567092
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.by1', '288.bx1', '288.iu1', '288.jb1', '288.jg1'], 'contains': ['1152.q1', '1152.k1', '1728.be1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 127370880, 93405314676], 'label': '6912.ia.576.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '576.cv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.df1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567093
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cl1', '288.i1', '288.jt1', '288.is1', '288.kc1', '288.kd1', '288.kf1', '288.kh1', '288.kk1', '288.lx1'], 'contains': ['1152.o1', '1152.r1', '1728.bk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 93405312000, 87091200], 'label': '6912.ia.576.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.cw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.du1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567094
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cl1', '288.j1', '288.jh1', '288.it1', '288.kb1', '288.ke1', '288.kg1', '288.ki1', '288.kl1', '288.ly1'], 'contains': ['1152.p1', '1152.s1', '1728.bk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7657413, 2676, 87091200], 'label': '6912.ia.576.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.cx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567095
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '12.by1', '12.cf1'], 'contains': ['48.bq1', '48.bx1', '48.cn1', '72.jt1', '72.ju1', '96.cd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.24.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567096
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cl1', '288.k1', '288.iu1', '288.kj1', '288.km1', '288.lz1'], 'contains': ['1152.q1', '1152.t1', '1728.bk1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 93405314676, 87091200], 'label': '6912.ia.576.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '576.cy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567097
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cm1', '288.l1', '288.iq1', '288.jn1', '288.kb1', '288.kn1', '288.ko1', '288.kp1', '288.kq1', '288.kr1'], 'contains': ['1152.p1', '1152.v1', '1728.bl1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2676, 87305699013, 40279680], 'label': '6912.ia.576.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.cz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567098
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cm1', '288.e1', '288.m1', '288.ir1', '288.kc1', '288.ks1', '288.kt1', '288.ku1', '288.kv1', '288.kw1'], 'contains': ['1152.o1', '1152.w1', '1728.bl1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87305699013, 40279680], 'label': '6912.ia.576.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.da1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567099
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cn1', '288.n1', '288.ju1', '288.iv1', '288.kd1', '288.ks1', '288.kx1', '288.ky1', '288.kz1', '288.ma1'], 'contains': ['1152.o1', '1152.x1', '1152.bf1', '1728.bm1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 40280426, 40279680], 'label': '6912.ia.576.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.db1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567100
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cn1', '288.o1', '288.ji1', '288.iw1', '288.ke1', '288.kn1', '288.la1', '288.lb1', '288.lc1', '288.md1'], 'contains': ['1152.p1', '1152.ba1', '1152.bg1', '1728.bm1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40315919, 2676, 40279680], 'label': '6912.ia.576.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.dc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ea1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567101
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.co1', '288.p1', '288.jh1', '288.ix1', '288.ko1', '288.la1', '288.ld1', '288.le1', '288.lf1', '288.me1'], 'contains': ['1152.p1', '1152.bb1', '1728.bn1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185948613, 2676, 87091200], 'label': '6912.ia.576.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.dd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567102
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.co1', '288.q1', '288.jt1', '288.iy1', '288.kt1', '288.kx1', '288.lg1', '288.lh1', '288.li1', '288.mf1'], 'contains': ['1152.o1', '1152.bc1', '1728.bn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87185948613, 87091200], 'label': '6912.ia.576.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.de1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ec1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567103
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cp1', '288.r1', '288.jv1', '288.iv1', '288.kf1', '288.ku1', '288.lg1', '288.lj1', '288.lk1', '288.ma1'], 'contains': ['1152.o1', '1152.bf1', '1728.bo1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87096887, 40279680], 'label': '6912.ia.576.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.df1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ed1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567104
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cp1', '288.s1', '288.jj1', '288.iw1', '288.kg1', '288.kp1', '288.ld1', '288.ll1', '288.lm1', '288.md1'], 'contains': ['1152.p1', '1152.bg1', '1728.bo1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40304216, 87105687, 40279680], 'label': '6912.ia.576.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.dg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ee1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567105
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cq1', '288.t1', '288.ju1', '288.iz1', '288.kh1', '288.ku1', '288.lh1', '288.ln1', '288.lo1', '288.mj1'], 'contains': ['1152.o1', '1152.bi1', '1152.bp1', '1728.bp1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87218571626, 40279680], 'label': '6912.ia.576.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.dh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ef1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567106
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '12.bz1', '12.cf1'], 'contains': ['48.bq1', '48.cc1', '48.co1', '72.jv1', '72.jw1', '96.ce1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243567107
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cq1', '288.u1', '288.ji1', '288.ja1', '288.ki1', '288.kp1', '288.le1', '288.lp1', '288.lq1', '288.mk1'], 'contains': ['1152.p1', '1152.bj1', '1152.bq1', '1728.bp1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2676, 87218607119, 40279680], 'label': '6912.ia.576.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.di1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567108
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cq1', '288.v1', '288.jb1', '288.kj1', '288.lr1', '288.ml1'], 'contains': ['1152.q1', '1152.bk1', '1152.br1', '1728.bp1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405314676, 87218607119, 40279680], 'label': '6912.ia.576.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.dj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567109
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cr1', '288.w1', '288.jw1', '288.jc1', '288.kd1', '288.kv1', '288.lh1', '288.lj1', '288.ls1', '288.mm1'], 'contains': ['1152.o1', '1152.bl1', '1728.bq1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87091200, 83468087], 'label': '6912.ia.576.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.dk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ei1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567110
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cr1', '288.x1', '288.jk1', '288.jd1', '288.ke1', '288.kq1', '288.le1', '288.ll1', '288.lt1', '288.mn1'], 'contains': ['1152.p1', '1152.bm1', '1728.bq1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [24536, 83476887, 87091200], 'label': '6912.ia.576.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.dl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ej1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567111
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cs1', '288.y1', '288.jv1', '288.iz1', '288.kk1', '288.ks1', '288.li1', '288.ls1', '288.lu1', '288.mj1'], 'contains': ['1152.o1', '1152.bp1', '1728.br1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87265388087, 40279680], 'label': '6912.ia.576.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.dm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ek1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567112
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cs1', '288.z1', '288.jj1', '288.ja1', '288.kl1', '288.kn1', '288.lf1', '288.lt1', '288.lv1', '288.mk1'], 'contains': ['1152.p1', '1152.bq1', '1728.br1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40304216, 87265388087, 40279680], 'label': '6912.ia.576.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.dn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.el1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567113
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cs1', '288.ba1', '288.jb1', '288.km1', '288.lw1', '288.ml1'], 'contains': ['1152.q1', '1152.br1', '1728.br1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93445616216, 87265388087, 40279680], 'label': '6912.ia.576.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.do1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.em1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567114
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.ct1', '288.bb1', '288.jw1', '288.je1', '288.kh1', '288.kw1', '288.kx1', '288.lk1', '288.lu1', '288.mq1'], 'contains': ['1152.o1', '1152.bs1', '1728.bs1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87261759287, 87091200], 'label': '6912.ia.576.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.dp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.en1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567115
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ct1', '288.bc1', '288.jk1', '288.jf1', '288.ki1', '288.kr1', '288.la1', '288.lm1', '288.lv1', '288.mr1'], 'contains': ['1152.p1', '1152.bt1', '1728.bs1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87261768087, 24536, 87091200], 'label': '6912.ia.576.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.dq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567116
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ct1', '288.bd1', '288.jg1', '288.kj1', '288.lw1', '288.mt1'], 'contains': ['1152.q1', '1152.bv1', '1728.bs1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405336536, 87261768087, 87091200], 'label': '6912.ia.576.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.dr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567117
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.bp1', '12.bu1', '12.bv1', '12.cc1', '12.cd1', '12.cr1', '12.cs1', '18.ba1', '18.bk1', '24.df1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 87178291200, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.6.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567118
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '12.by1', '12.cg1'], 'contains': ['48.bq1', '48.cg1', '48.cp1', '72.jx1', '72.jy1', '72.jz1', '96.cf1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87298051065, 127370880, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567119
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cu1', '288.bf1', '288.jx1', '288.is1', '288.kt1', '288.ky1', '288.lj1', '288.ln1', '288.lu1', '288.lx1'], 'contains': ['1152.o1', '1728.bt1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 43945413, 87091200], 'label': '6912.ia.576.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.ds1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567120
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.eg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cv1', '288.bi1', '288.jx1', '288.iy1', '288.kc1', '288.kz1', '288.lk1', '288.lo1', '288.ls1', '288.mf1'], 'contains': ['1152.o1', '1728.bu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87222236613, 87091200], 'label': '6912.ia.576.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.dt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.er1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567121
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cw1', '288.bm1', '288.jy1', '288.jc1', '288.kf1', '288.kw1', '288.ky1', '288.li1', '288.lo1', '288.mm1'], 'contains': ['1152.o1', '1728.bv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43909226, 93405312000, 87091200], 'label': '6912.ia.576.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.du1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.es1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567122
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cx1', '288.bp1', '288.jy1', '288.je1', '288.kk1', '288.kv1', '288.kz1', '288.lg1', '288.ln1', '288.mq1'], 'contains': ['1152.o1', '1728.bw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87222200426, 87091200], 'label': '6912.ia.576.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.dv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.et1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567123
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cu1', '288.bq1', '288.jl1', '288.it1', '288.ko1', '288.lb1', '288.ll1', '288.lp1', '288.lv1', '288.ly1'], 'contains': ['1152.p1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [43945413, 2676, 87091200], 'label': '6912.ia.576.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.dw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.eu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567124
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cv1', '288.br1', '288.jl1', '288.ix1', '288.kb1', '288.lc1', '288.lm1', '288.lq1', '288.lt1', '288.me1'], 'contains': ['1152.p1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87222236613, 2676, 87091200], 'label': '6912.ia.576.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.dx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ev1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567125
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cw1', '288.bs1', '288.jm1', '288.jd1', '288.kg1', '288.kr1', '288.lb1', '288.lf1', '288.lq1', '288.mn1'], 'contains': ['1152.p1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [43944719, 2676, 87091200], 'label': '6912.ia.576.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.dy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ew1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567126
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cx1', '288.bt1', '288.jm1', '288.jf1', '288.kl1', '288.kq1', '288.lc1', '288.ld1', '288.lp1', '288.mr1'], 'contains': ['1152.p1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87222235919, 2676, 87091200], 'label': '6912.ia.576.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.dz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ex1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567128
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.cx1', '288.bv1', '288.jg1', '288.km1', '288.lr1', '288.mt1'], 'contains': ['1152.q1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87222235919, 93405314676, 87091200], 'label': '6912.ia.576.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.eb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ez1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567129
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '12.bz1', '12.cg1', '12.ch1', '12.ci1', '12.cj1', '12.ck1'], 'contains': ['48.bq1', '48.cm1', '72.ka1', '72.kb1', '72.kc1', '96.cg1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.24.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243567130
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cy1', '192.da1', '192.db1', '288.bw1', '288.jn1', '288.ly1', '288.md1', '288.me1', '288.mk1', '288.mn1', '288.mr1'], 'contains': ['1152.p1', '1728.a1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 2676, 40279680], 'label': '6912.ia.576.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '576.ec1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fa1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567131
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cy1', '192.dc1', '192.dd1', '288.bx1', '288.lz1', '288.ml1', '288.mt1'], 'contains': ['1152.q1', '1728.a1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [127370880, 93405314676, 40279680], 'label': '6912.ia.576.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '576.ed1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567132
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '192.db1', '192.dd1', '288.by1', '288.mc1', '288.mh1', '288.mu1'], 'contains': ['1728.a1', '2304.e1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [127370880, 93452849280, 40279680], 'label': '6912.ia.576.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '576.ee1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567133
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cz1', '192.da1', '192.dd1', '288.bz1', '288.jp1', '288.mp1', '288.mv1'], 'contains': ['1728.a1', '2304.f1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 127370880, 40279680], 'label': '6912.ia.576.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '576.ef1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567134
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cz1', '192.db1', '192.dc1', '192.dd1', '288.ca1', '288.mw1'], 'contains': ['1728.a1', '2304.g1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [127370880, 93525428474, 40279680], 'label': '6912.ia.576.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '576.eg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fe1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567135
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bp1', '288.i1', '288.hu1', '288.hz1', '288.ib1'], 'contains': ['1152.i1', '1152.r1', '1728.t1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 7657413, 87128133], 'label': '6912.ia.576.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.eh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567136
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bp1', '288.j1', '288.hq1', '288.ia1', '288.ic1'], 'contains': ['1152.j1', '1152.s1', '1728.t1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7657413, 87128133, 2676], 'label': '6912.ia.576.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.ei1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567137
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bp1', '288.k1', '288.id1'], 'contains': ['1152.k1', '1152.t1', '1728.t1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7657413, 87128133, 93405314676], 'label': '6912.ia.576.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '576.ej1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ch1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567138
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ft1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bq1', '288.l1', '288.iq1', '288.ie1', '288.if1'], 'contains': ['1152.j1', '1152.v1', '1728.u1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 2676, 87305699013], 'label': '6912.ia.576.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '576.ek1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ci1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567139
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bq1', '288.m1', '288.ir1', '288.ig1', '288.ih1'], 'contains': ['1152.i1', '1152.w1', '1728.u1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40316613, 93405312000, 87305699013], 'label': '6912.ia.576.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '576.el1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567140
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bh1', '8.g1', '12.bn1'], 'contains': ['48.x1', '48.z1', '48.ba1', '48.be1', '48.br1', '48.bu1', '48.cf1', '48.fp1', '48.gq1', '72.jq1', '72.kd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.24.ca1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567141
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.br1', '288.n1', '288.hv1', '288.iv1', '288.hz1', '288.ig1', '288.ii1'], 'contains': ['1152.i1', '1152.x1', '1152.bf1', '1728.v1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 40315919], 'label': '6912.ia.576.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.em1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ck1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567142
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.br1', '288.o1', '288.hr1', '288.iw1', '288.ia1', '288.ie1', '288.ij1'], 'contains': ['1152.j1', '1152.ba1', '1152.bg1', '1728.v1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 40280426, 2676], 'label': '6912.ia.576.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '576.en1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567143
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bs1', '288.p1', '288.hq1', '288.ij1', '288.ik1'], 'contains': ['1152.j1', '1152.bb1', '1728.w1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87185948613, 87128133, 2676], 'label': '6912.ia.576.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.eo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567144
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bs1', '288.q1', '288.hu1', '288.ii1', '288.il1'], 'contains': ['1152.i1', '1152.bc1', '1728.w1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93405312000, 87185948613, 87128133], 'label': '6912.ia.576.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.ep1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567145
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bt1', '288.r1', '288.hw1', '288.iv1', '288.ih1', '288.im1', '288.in1'], 'contains': ['1152.i1', '1152.bf1', '1728.x1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 87105687], 'label': '6912.ia.576.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gr1', 'old_label': '576.eq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.co1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567146
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bt1', '288.s1', '288.hs1', '288.iw1', '288.if1'], 'contains': ['1152.j1', '1152.bg1', '1728.x1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 40310618, 87096887], 'label': '6912.ia.576.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bg1', 'old_label': '576.er1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567147
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bu1', '288.t1', '288.hv1', '288.iz1', '288.ib1', '288.ih1', '288.il1'], 'contains': ['1152.i1', '1152.bi1', '1152.bp1', '1728.y1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 87218607119], 'label': '6912.ia.576.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.es1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567148
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.bu1', '288.u1', '288.hr1', '288.ja1', '288.ic1', '288.if1', '288.ik1'], 'contains': ['1152.j1', '1152.bj1', '1152.bq1', '1728.y1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 87218571626, 2676], 'label': '6912.ia.576.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.et1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567149
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.bu1', '288.v1', '288.jb1', '288.id1'], 'contains': ['1152.k1', '1152.bk1', '1152.br1', '1728.y1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 87218571626, 93405314676], 'label': '6912.ia.576.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '576.eu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567150
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bv1', '288.w1', '288.hx1', '288.hz1', '288.il1', '288.im1', '288.io1'], 'contains': ['1152.i1', '1152.bl1', '1728.z1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87128133, 83476887], 'label': '6912.ia.576.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '576.ev1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567151
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bi1', '8.g1', '12.bl1'], 'contains': ['48.bs1', '48.bv1', '48.ci1', '48.gr1', '72.jr1', '72.kd1', '96.ci1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.cb1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567152
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bv1', '288.x1', '288.ht1', '288.ia1', '288.ik1'], 'contains': ['1152.j1', '1152.bm1', '1728.z1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [24536, 87128133, 83476887], 'label': '6912.ia.576.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.ew1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567153
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bw1', '288.y1', '288.hw1', '288.iz1', '288.ig1', '288.io1', '288.ip1'], 'contains': ['1152.i1', '1152.bp1', '1728.ba1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 93405312000, 87265396887], 'label': '6912.ia.576.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gr1', 'old_label': '576.ex1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567154
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bw1', '288.z1', '288.hs1', '288.ja1', '288.ie1'], 'contains': ['1152.j1', '1152.bq1', '1728.ba1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40316613, 40310618, 87265388087], 'label': '6912.ia.576.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '576.ey1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567155
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bw1', '288.ba1', '288.jb1'], 'contains': ['1152.k1', '1152.br1', '1728.ba1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40316613, 93445622618, 87265388087], 'label': '6912.ia.576.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.gk1', 'old_label': '576.ez1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567156
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bx1', '288.bb1', '288.hx1', '288.ib1', '288.ii1', '288.in1', '288.ip1'], 'contains': ['1152.i1', '1152.bs1', '1728.bb1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87261768087, 87128133], 'label': '6912.ia.576.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '576.fa1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567157
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bx1', '288.bc1', '288.ht1', '288.ic1', '288.ij1'], 'contains': ['1152.j1', '1152.bt1', '1728.bb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87261768087, 24536, 87128133], 'label': '6912.ia.576.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.fb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567158
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.bx1', '288.bd1', '288.id1'], 'contains': ['1152.k1', '1152.bv1', '1728.bb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405336536, 87261768087, 87128133], 'label': '6912.ia.576.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '576.fc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.da1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567159
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.hy1', '288.im1', '288.ip1'], 'contains': ['1152.i1', '1728.bc1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 93405312000, 87128133], 'label': '6912.ia.576.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '576.fd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.db1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567160
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bo1', '288.hy1', '288.in1', '288.io1'], 'contains': ['1152.i1', '1728.bd1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87222232609, 93405312000, 87128133], 'label': '6912.ia.576.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '576.fe1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243567161
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.de1', '288.cs1', '288.jh1', '288.hq1', '288.mx1', '288.my1'], 'contains': ['1152.s1', '1152.v1', '1152.bb1', '1728.bx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87265419333, 2676], 'label': '6912.ia.576.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.ff1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ff1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567162
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bj1', '8.g1'], 'contains': ['48.bt1', '48.bw1', '48.cj1', '48.gs1', '72.js1', '72.kd1', '96.cj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87185911680, 87222200426, 36933, 40279680], 'label': '6912.ia.24.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '24.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567163
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.de1', '288.ct1', '288.jt1', '288.hu1', '288.mz1', '288.na1'], 'contains': ['1152.r1', '1152.w1', '1152.bc1', '1728.bx1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 87265419333], 'label': '6912.ia.576.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '576.fg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567164
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.df1', '192.dj1', '288.cu1', '288.jz1', '288.kd1', '288.hz1', '288.mz1'], 'contains': ['1152.r1', '1152.x1', '1152.bl1', '1728.by1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 7621226], 'label': '6912.ia.576.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.fh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567165
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.df1', '192.dk1', '288.cv1', '288.jq1', '288.ke1', '288.ia1', '288.mx1'], 'contains': ['1152.s1', '1152.ba1', '1152.bm1', '1728.by1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7657413, 7621226, 2676], 'label': '6912.ia.576.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.fi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567166
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dg1', '288.cw1', '288.ka1', '288.kd1', '288.hz1', '288.na1'], 'contains': ['1152.r1', '1152.bf1', '1152.bl1', '1728.bz1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 83468087], 'label': '6912.ia.576.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.fj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567167
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dg1', '288.cx1', '288.jr1', '288.ke1', '288.ia1', '288.my1'], 'contains': ['1152.s1', '1152.bg1', '1152.bm1', '1728.bz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6851, 7657413, 83468087], 'label': '6912.ia.576.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '576.fk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567168
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dh1', '192.dl1', '288.cy1', '288.jz1', '288.kh1', '288.ib1', '288.na1'], 'contains': ['1152.r1', '1152.bi1', '1152.bs1', '1728.ca1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 87185912426], 'label': '6912.ia.576.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.fl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567169
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dh1', '192.dm1', '288.cz1', '288.jq1', '288.ki1', '288.ic1', '288.my1'], 'contains': ['1152.s1', '1152.bj1', '1152.bt1', '1728.ca1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 87185947919, 2676], 'label': '6912.ia.576.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.fm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567170
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dh1', '192.dn1', '288.da1', '288.kj1', '288.id1'], 'contains': ['1152.t1', '1152.bk1', '1152.bv1', '1728.ca1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 87185947919, 93405314676], 'label': '6912.ia.576.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '576.fn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567171
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.di1', '288.db1', '288.ka1', '288.kh1', '288.ib1', '288.mz1'], 'contains': ['1152.r1', '1152.bp1', '1152.bs1', '1728.cb1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 7657413, 87261759287], 'label': '6912.ia.576.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.fo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567172
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.di1', '288.dc1', '288.jr1', '288.ki1', '288.ic1', '288.mx1'], 'contains': ['1152.s1', '1152.bq1', '1152.bt1', '1728.cb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 6851, 87261768087], 'label': '6912.ia.576.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.fp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567173
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bk1', '8.h1', '12.bl1'], 'contains': ['48.bv1', '48.by1', '48.ce1', '48.gt1', '72.ke1', '72.kf1', '96.cl1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.24.cd1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567174
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.di1', '288.dd1', '288.kj1', '288.id1'], 'contains': ['1152.t1', '1152.br1', '1152.bv1', '1728.cb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [7620480, 87261768087, 93405318851], 'label': '6912.ia.576.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '576.fq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567175
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.rc1', '192.dj1', '192.dk1', '288.di1', '288.js1'], 'contains': ['1152.u1', '1152.y1', '1152.bn1', '1728.by1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7657413, 47537280, 7621226], 'label': '6912.ia.576.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '576.fr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567176
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.rd1', '192.dl1', '192.dm1', '192.dn1', '288.dj1', '288.js1'], 'contains': ['1152.u1', '1152.bh1', '1152.bu1', '1728.ca1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7620480, 47537280, 87185912426], 'label': '6912.ia.576.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '576.fs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567177
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.do1', '288.dm1', '288.ji1', '288.hr1', '288.kn1', '288.ie1', '288.mx1'], 'contains': ['1152.v1', '1152.ba1', '1152.bq1', '1728.cc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 746, 2676], 'label': '6912.ia.576.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.ft1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ft1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567178
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dp1', '288.dn1', '288.ji1', '288.hr1', '288.kp1', '288.if1', '288.my1'], 'contains': ['1152.v1', '1152.bg1', '1152.bj1', '1728.cd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 40280426, 2676], 'label': '6912.ia.576.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '576.fu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567179
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dq1', '288.do1', '288.jj1', '288.hs1', '288.kn1', '288.kp1', '288.ie1', '288.if1'], 'contains': ['1152.v1', '1152.bg1', '1152.bq1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87218607813, 6851, 87096887], 'label': '6912.ia.576.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.iu1', 'old_label': '576.fv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567180
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dr1', '288.dp1', '288.jk1', '288.ht1', '288.mx1', '288.my1'], 'contains': ['1152.v1', '1152.bm1', '1152.bt1', '1728.cf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6851, 87265419333, 83468087], 'label': '6912.ia.576.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.fw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567181
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.do1', '288.dq1', '288.ju1', '288.hv1', '288.ks1', '288.ig1', '288.mz1'], 'contains': ['1152.w1', '1152.x1', '1152.bp1', '1728.cc1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [36239, 87218607813, 93405312000], 'label': '6912.ia.576.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.fx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567182
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dp1', '288.dr1', '288.ju1', '288.hv1', '288.ku1', '288.ih1', '288.na1'], 'contains': ['1152.w1', '1152.bf1', '1152.bi1', '1728.cd1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218607813, 93405312000, 40315919], 'label': '6912.ia.576.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '576.fy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567183
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dq1', '288.ds1', '288.jv1', '288.hw1', '288.ks1', '288.ku1', '288.ig1', '288.ih1'], 'contains': ['1152.w1', '1152.bf1', '1152.bp1', '1728.ce1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87218607813, 93405312000, 87105687], 'label': '6912.ia.576.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jb1', 'old_label': '576.fz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.fz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567184
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bl1', '8.h1', '12.bn1'], 'contains': ['48.bb1', '48.bc1', '48.bg1', '48.bh1', '48.bu1', '48.ca1', '48.cb1', '48.fq1', '48.gu1', '72.ke1', '72.kg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.24.ce1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567185
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dr1', '288.dt1', '288.jw1', '288.hx1', '288.mz1', '288.na1'], 'contains': ['1152.w1', '1152.bl1', '1152.bs1', '1728.cf1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 83476887, 87265419333], 'label': '6912.ia.576.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.ga1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ga1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567186
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ds1', '192.dt1', '288.dy1', '288.jz1', '288.kx1', '288.ii1', '288.mz1'], 'contains': ['1152.x1', '1152.bc1', '1152.bs1', '1728.cg1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 87185948613, 87185912426], 'label': '6912.ia.576.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.gb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567187
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.rf1', '192.ds1', '192.du1', '288.dz1', '288.js1'], 'contains': ['1152.y1', '1152.bd1', '1152.bu1', '1728.cg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [47537280, 87185948613, 87185912426], 'label': '6912.ia.576.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '576.gc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567188
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.rg1', '192.ds1', '192.dv1', '288.ea1'], 'contains': ['1152.z1', '1152.be1', '1152.bw1', '1728.cg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [87185911680, 93452849280, 87185912426], 'label': '6912.ia.576.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '576.gd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567189
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dt1', '192.du1', '192.dv1', '288.en1', '288.jq1', '288.la1', '288.ij1', '288.mx1'], 'contains': ['1152.ba1', '1152.bb1', '1152.bt1', '1728.cg1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [87185947919, 87185911680, 2676], 'label': '6912.ia.576.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.ge1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ge1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567190
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dw1', '288.eo1', '288.jr1', '288.la1', '288.ij1', '288.my1'], 'contains': ['1152.bb1', '1152.bg1', '1152.bt1', '1728.ch1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6851, 87185911680, 87261768087], 'label': '6912.ia.576.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.gf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567191
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dx1', '192.dy1', '288.ep1', '288.jq1', '288.le1', '288.ik1', '288.my1'], 'contains': ['1152.bb1', '1152.bj1', '1152.bm1', '1728.ci1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [7656719, 87185911680, 2676], 'label': '6912.ia.576.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.gg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567192
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.dz1', '288.eq1', '288.jr1', '288.le1', '288.ik1', '288.mx1'], 'contains': ['1152.bb1', '1152.bm1', '1152.bq1', '1728.cj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6851, 87185911680, 83476887], 'label': '6912.ia.576.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '576.gh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567193
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dw1', '288.er1', '288.ka1', '288.kx1', '288.ii1', '288.na1'], 'contains': ['1152.bc1', '1152.bf1', '1152.bs1', '1728.ch1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 87185948613, 87261759287], 'label': '6912.ia.576.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.gi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567194
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.rj1', '192.dx1', '192.ea1', '288.es1', '288.js1'], 'contains': ['1152.bd1', '1152.bh1', '1152.bn1', '1728.ci1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [47537280, 87185948613, 7621226], 'label': '6912.ia.576.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '576.gj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567195
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '12.bo1', '12.cf1', '12.cp1'], 'contains': ['48.c1', '48.bx1', '48.cc1', '48.gv1', '72.kf1', '72.kg1', '96.co1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 87185911680, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.cf1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567196
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dy1', '192.ea1', '288.et1', '288.jz1', '288.lh1', '288.il1', '288.na1'], 'contains': ['1152.bc1', '1152.bi1', '1152.bl1', '1728.ci1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 87185948613, 7621226], 'label': '6912.ia.576.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.gk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567197
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '576.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.dz1', '288.eu1', '288.ka1', '288.lh1', '288.il1', '288.mz1'], 'contains': ['1152.bc1', '1152.bl1', '1152.bp1', '1728.cj1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405312000, 87185948613, 83468087], 'label': '6912.ia.576.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '576.gl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.gl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567198
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.a1', '384.a1', '384.j1', '384.m1', '384.h1', '384.n1', '384.r1', '384.t1', '384.w1', '384.ba1', '384.be1', '384.bf1', '384.bj1', '384.bk1'], 'contains': ['2304.a1', '2304.b1', '2304.d1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 2676], 'label': '6912.ia.768.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '768.a1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567199
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '256.a1', '384.b1', '384.k1', '384.o1', '384.s1', '384.z1', '384.bb1', '384.bg1', '384.bl1'], 'contains': ['2304.a1', '2304.c1', '2304.e1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [93405312000, 47537280], 'label': '6912.ia.768.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '768.b1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567200
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.cz1', '256.a1', '384.c1', '384.l1', '384.bh1', '384.bm1'], 'contains': ['2304.a1', '2304.f1', '2304.g1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120116474, 93405312000], 'label': '6912.ia.768.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '768.c1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567201
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.da1', '256.a1', '384.d1', '384.i1', '384.p1', '384.u1', '384.x1', '384.bc1', '384.bi1', '384.bn1'], 'contains': ['2304.b1', '2304.c1', '2304.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 47537280], 'label': '6912.ia.768.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '768.d1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567202
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.db1', '256.a1', '384.e1', '384.v1', '384.y1', '384.bo1'], 'contains': ['2304.b1', '2304.e1', '2304.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [174404119680, 93525427956], 'label': '6912.ia.768.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '768.e1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567203
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.dc1', '256.a1', '384.f1', '384.q1', '384.bd1', '384.bp1'], 'contains': ['2304.c1', '2304.d1', '2304.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [93525427956, 47537280], 'label': '6912.ia.768.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '768.f1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567204
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '768.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.dd1', '256.a1', '384.g1', '384.bq1'], 'contains': ['2304.d1', '2304.e1', '2304.f1', '2304.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120115956, 93452849280], 'label': '6912.ia.768.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.g1', 'old_label': '768.g1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567205
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '288.b1', '288.bw1', '288.bx1', '288.by1', '288.bz1', '288.ca1', '432.eh1', '432.ei1', '432.ej1', '432.ek1', '432.el1', '432.em1', '432.en1', '432.eo1', '432.ep1', '432.eq1', '432.er1'], 'contains': ['1728.a1', '1728.b1', '1728.be1'], 'core': '864.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 36933, 40279680], 'label': '6912.ia.864.a1', 'mobius_quo': 1, 'mobius_sub': -864, 'normal_closure': '864.a1', 'normal_contained_in': ['216.a1', '288.a1', '288.b1'], 'normal_contains': ['1728.a1', '3456.a1'], 'normalizer': '1.a1', 'old_label': '864.a1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '864.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567206
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.bp1', '12.cg1', '12.cp1', '12.cq1', '12.cr1', '12.cs1'], 'contains': ['48.c1', '48.cm1', '48.cp1', '72.kh1', '72.kj1', '72.kl1', '96.cp1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567207
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': ['8.p1'], 'conjugacy_class_count': 1, 'contained_in': ['288.c1', '288.d1', '288.hf1', '288.hh1', '288.hl1', '288.hm1', '288.ho1', '432.fj1', '432.ds1', '432.gi1', '432.hc1', '432.hp1', '432.id1', '432.im1', '432.iu1', '432.jc1', '432.jm1', '432.jw1'], 'contains': ['1728.m1'], 'core': '864.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 32929, 36933], 'label': '6912.ia.864.b1', 'mobius_quo': 0, 'mobius_sub': -864, 'normal_closure': '864.b1', 'normal_contained_in': ['216.a1', '288.c1', '288.d1'], 'normal_contains': ['3456.a1'], 'normalizer': '1.a1', 'old_label': '864.b1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '864.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567208
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.g1', '288.h1', '432.a1', '432.b1', '432.c1', '432.d1', '432.e1', '432.f1', '432.g1', '432.i1', '432.h1', '432.j1', '432.eh1'], 'contains': ['1728.c1', '1728.b1', '1728.e1', '1728.bf1', '1728.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 40279680], 'label': '6912.ia.864.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567209
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cb1', '288.cc1', '288.cl1', '432.a1', '432.es1', '432.et1', '432.eu1', '432.ev1'], 'contains': ['1728.c1', '1728.d1', '1728.g1', '1728.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 87178291200, 36933], 'label': '6912.ia.864.y1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567210
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.ge1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cd1', '288.ce1', '288.cm1', '432.b1', '432.es1', '432.ew1', '432.ex1', '432.ey1'], 'contains': ['1728.c1', '1728.f1', '1728.i1', '1728.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87178291200, 36933, 746], 'label': '6912.ia.864.z1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '864.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567211
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '288.cn1', '432.b1', '432.c1', '432.et1', '432.ew1', '432.ez1', '432.fa1', '432.fb1'], 'contains': ['1728.c1', '1728.h1', '1728.k1', '1728.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 87178291200, 36933], 'label': '6912.ia.864.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567212
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cg1', '288.ch1', '288.ci1', '288.co1', '432.d1', '432.es1', '432.et1', '432.ex1', '432.ez1', '432.fc1', '432.fd1'], 'contains': ['1728.c1', '1728.j1', '1728.l1', '1728.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87178291200, 36933, 83468087], 'label': '6912.ia.864.bb1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567213
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cj1', '288.cp1', '432.e1', '432.eu1', '432.ey1', '432.fa1', '432.fc1', '432.fe1', '432.ff1', '432.fg1', '432.fh1', '432.fi1', '432.fj1'], 'contains': ['1728.c1', '1728.m1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87178291200, 36933], 'label': '6912.ia.864.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567214
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cq1', '432.e1', '432.g1', '432.ev1', '432.ew1', '432.fb1', '432.fd1', '432.fe1', '432.fk1', '432.fl1', '432.fm1'], 'contains': ['1728.c1', '1728.n1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87178291200, 127403809, 36933], 'label': '6912.ia.864.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567215
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ck1', '288.cr1', '432.h1', '432.eu1', '432.ev1', '432.ex1', '432.ez1', '432.ff1', '432.fk1'], 'contains': ['1728.c1', '1728.p1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178291200, 36933, 83495329], 'label': '6912.ia.864.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567216
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.i1', '288.j1', '288.k1', '432.a1', '432.k1', '432.l1', '432.m1', '432.n1', '432.o1', '432.p1', '432.r1', '432.q1', '432.s1', '432.ei1'], 'contains': ['1728.b1', '1728.d1', '1728.bk1', '1728.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 36933, 87091200], 'label': '6912.ia.864.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567217
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '12.cf1', '12.cq1'], 'contains': ['48.c1', '48.cn1', '48.co1', '72.ki1', '72.kk1', '96.cq1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43941409, 127370880, 87218603809, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567218
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.l1', '288.m1', '432.eh1', '432.k1', '432.t1', '432.u1', '432.v1', '432.w1', '432.x1', '432.y1', '432.z1', '432.bb1', '432.ba1'], 'contains': ['1728.b1', '1728.e1', '1728.bl1', '1728.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87305662080, 36933, 40279680], 'label': '6912.ia.864.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567219
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.n1', '288.o1', '432.b1', '432.l1', '432.t1', '432.bc1', '432.bd1', '432.be1', '432.bf1', '432.bg1', '432.bh1', '432.bi1', '432.bj1', '432.bk1', '432.bl1', '432.bm1', '432.ej1'], 'contains': ['1728.b1', '1728.f1', '1728.h1', '1728.bm1', '1728.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40280426, 36933, 40279680], 'label': '6912.ia.864.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '864.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567220
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.q1', '432.a1', '432.u1', '432.bc1', '432.bn1', '432.bo1', '432.bp1', '432.bq1', '432.bs1', '432.br1', '432.bt1', '432.ek1'], 'contains': ['1728.b1', '1728.g1', '1728.bn1', '1728.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 87091200], 'label': '6912.ia.864.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567221
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.r1', '288.s1', '432.c1', '432.m1', '432.v1', '432.bl1', '432.bn1', '432.bu1', '432.bv1', '432.bw1', '432.bx1', '432.by1', '432.bz1', '432.ca1', '432.cb1', '432.cc1', '432.ej1'], 'contains': ['1728.b1', '1728.h1', '1728.bo1', '1728.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 87096887, 40279680], 'label': '6912.ia.864.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '864.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567222
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.t1', '288.u1', '288.v1', '432.b1', '432.n1', '432.v1', '432.bd1', '432.bo1', '432.bu1', '432.cd1', '432.ce1', '432.cf1', '432.cg1', '432.ch1', '432.ci1', '432.cj1', '432.ck1', '432.el1'], 'contains': ['1728.b1', '1728.i1', '1728.k1', '1728.bp1', '1728.y1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218571626, 36933, 40279680], 'label': '6912.ia.864.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567223
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.w1', '288.x1', '432.d1', '432.l1', '432.w1', '432.be1', '432.bo1', '432.bv1', '432.bw1', '432.cd1', '432.cl1', '432.cm1', '432.cn1', '432.co1', '432.cp1', '432.cq1', '432.em1'], 'contains': ['1728.b1', '1728.j1', '1728.bq1', '1728.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 87091200, 83468087], 'label': '6912.ia.864.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '864.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567224
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.y1', '288.z1', '288.ba1', '432.c1', '432.o1', '432.t1', '432.bf1', '432.bp1', '432.bx1', '432.cj1', '432.cl1', '432.cm1', '432.cr1', '432.cs1', '432.ct1', '432.cu1', '432.cv1', '432.el1'], 'contains': ['1728.b1', '1728.k1', '1728.br1', '1728.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87265388087, 40279680], 'label': '6912.ia.864.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567225
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1', '288.bc1', '288.bd1', '432.d1', '432.n1', '432.x1', '432.bc1', '432.bg1', '432.by1', '432.bz1', '432.ce1', '432.cn1', '432.cr1', '432.cs1', '432.cw1', '432.cx1', '432.cy1', '432.en1'], 'contains': ['1728.b1', '1728.l1', '1728.bs1', '1728.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87261759287, 87091200], 'label': '6912.ia.864.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567226
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.be1', '432.e1', '432.p1', '432.y1', '432.bm1', '432.bq1', '432.cc1', '432.ck1', '432.cq1', '432.cv1', '432.cy1', '432.cz1', '432.da1', '432.db1', '432.dd1', '432.dc1', '432.de1', '432.df1', '432.dg1', '432.dh1', '432.di1', '432.dj1', '432.dk1', '432.dl1', '432.dm1', '432.dn1', '432.do1', '432.dp1', '432.dq1', '432.dr1', '432.ds1', '432.eo1'], 'contains': ['1728.b1', '1728.m1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 32929, 36933], 'label': '6912.ia.864.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567227
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bf1', '288.bq1', '288.bu1', '432.f1', '432.u1', '432.bh1', '432.bv1', '432.cf1', '432.cr1', '432.cz1', '432.du1', '432.dt1', '432.dv1', '432.ei1'], 'contains': ['1728.b1', '1728.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43908480, 36933, 87091200], 'label': '6912.ia.864.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567228
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.br1', '12.bt1', '12.bv1', '12.ci1', '12.cj1', '12.cu1', '12.cv1', '18.bc1', '18.bm1', '24.dh1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87178291200, 47537280, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.6.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567229
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '12.by1', '12.cp1'], 'contains': ['48.bx1', '48.cc1', '48.cp1', '72.km1', '72.kp1', '96.cr1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87298051065, 127370880, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567230
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bh1', '432.e1', '432.r1', '432.z1', '432.bd1', '432.bs1', '432.bx1', '432.cn1', '432.da1', '432.du1', '432.ea1', '432.dw1', '432.ec1', '432.eb1', '432.ed1', '432.ep1'], 'contains': ['1728.b1', '1728.o1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218603809, 36933, 40279680], 'label': '6912.ia.864.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567231
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bi1', '288.br1', '432.f1', '432.k1', '432.bi1', '432.by1', '432.cg1', '432.cl1', '432.db1', '432.ea1', '432.dx1', '432.ee1', '432.ek1'], 'contains': ['1728.b1', '1728.bu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87222199680, 36933, 87091200], 'label': '6912.ia.864.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567232
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bg1', '432.g1', '432.q1', '432.z1', '432.bl1', '432.br1', '432.cj1', '432.co1', '432.cw1', '432.dr1', '432.dt1', '432.dw1', '432.dx1', '432.dy1', '432.dz1', '432.eo1'], 'contains': ['1728.b1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 36933, 87100665], 'label': '6912.ia.864.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567233
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '432.i1', '432.q1', '432.bb1', '432.bj1', '432.bt1', '432.bw1', '432.ch1', '432.cs1', '432.cz1', '432.dd1', '432.ea1', '432.ec1', '432.dy1', '432.eg1', '432.eq1'], 'contains': ['1728.b1', '1728.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 36933, 87091200], 'label': '6912.ia.864.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567234
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bj1', '432.h1', '432.p1', '432.ba1', '432.be1', '432.bs1', '432.ca1', '432.ce1', '432.ct1', '432.dc1', '432.dt1', '432.eb1', '432.ee1', '432.dy1', '432.ef1', '432.eq1'], 'contains': ['1728.b1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7653409, 36933, 87091200], 'label': '6912.ia.864.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567235
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bl1', '432.g1', '432.s1', '432.y1', '432.bf1', '432.bt1', '432.bu1', '432.cp1', '432.cx1', '432.de1', '432.dv1', '432.dw1', '432.ee1', '432.eg1', '432.ef1', '432.ep1'], 'contains': ['1728.b1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [36933, 87265415329, 40279680], 'label': '6912.ia.864.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567236
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bm1', '288.bs1', '432.j1', '432.m1', '432.x1', '432.bh1', '432.bj1', '432.bp1', '432.ca1', '432.cg1', '432.ci1', '432.co1', '432.cu1', '432.cx1', '432.df1', '432.ed1', '432.em1'], 'contains': ['1728.b1', '1728.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 36933, 87091200], 'label': '6912.ia.864.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '864.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567237
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bn1', '432.h1', '432.r1', '432.bb1', '432.bg1', '432.bq1', '432.cb1', '432.cd1', '432.cu1', '432.dg1', '432.dv1', '432.eb1', '432.dx1', '432.dz1', '432.eg1', '432.er1'], 'contains': ['1728.b1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87185944609, 36933, 87091200], 'label': '6912.ia.864.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567238
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bo1', '432.i1', '432.s1', '432.ba1', '432.bk1', '432.br1', '432.bz1', '432.ci1', '432.cm1', '432.db1', '432.dh1', '432.du1', '432.ec1', '432.dz1', '432.ef1', '432.er1'], 'contains': ['1728.b1', '1728.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87222232609, 36933, 87091200], 'label': '6912.ia.864.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567239
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bp1', '288.bt1', '288.bv1', '432.j1', '432.o1', '432.w1', '432.bi1', '432.bk1', '432.bn1', '432.cb1', '432.cf1', '432.ch1', '432.cp1', '432.ct1', '432.cw1', '432.di1', '432.ed1', '432.en1'], 'contains': ['1728.b1', '1728.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222200426, 36933, 87091200], 'label': '6912.ia.864.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567240
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '12.ca1', '12.cf1'], 'contains': ['48.bx1', '48.cg1', '48.co1', '72.kn1', '72.kq1', '96.cs1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 119759865, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567241
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cs1', '288.ct1', '432.a1', '432.fn1', '432.fo1', '432.fp1', '432.fq1'], 'contains': ['1728.d1', '1728.e1', '1728.g1', '1728.bx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 36933, 87265382400], 'label': '6912.ia.864.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567242
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cu1', '288.cv1', '288.di1', '432.es1', '432.l1', '432.fn1', '432.fr1', '432.fs1', '432.ft1', '432.fu1'], 'contains': ['1728.d1', '1728.f1', '1728.j1', '1728.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 7621226, 36933], 'label': '6912.ia.864.bg1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '864.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567243
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cw1', '288.cx1', '432.et1', '432.l1', '432.fo1', '432.fr1', '432.fv1', '432.fw1', '432.fx1'], 'contains': ['1728.d1', '1728.h1', '1728.j1', '1728.bz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 36933, 83468087], 'label': '6912.ia.864.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '864.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567244
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cy1', '288.cz1', '288.da1', '288.dj1', '432.es1', '432.n1', '432.fo1', '432.fs1', '432.fv1', '432.fy1', '432.fz1'], 'contains': ['1728.d1', '1728.i1', '1728.l1', '1728.ca1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 36933, 87185912426], 'label': '6912.ia.864.bi1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567245
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.db1', '288.dc1', '288.dd1', '432.et1', '432.n1', '432.fn1', '432.ft1', '432.fw1', '432.fy1', '432.ga1'], 'contains': ['1728.d1', '1728.k1', '1728.l1', '1728.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7620480, 36933, 87261759287], 'label': '6912.ia.864.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567246
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.de1', '288.dk1', '432.eu1', '432.p1', '432.fp1', '432.fu1', '432.fx1', '432.fz1', '432.ga1', '432.gc1', '432.gb1', '432.gd1', '432.ge1', '432.gf1', '432.gg1', '432.gh1', '432.gi1'], 'contains': ['1728.d1', '1728.m1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 32929, 36933], 'label': '6912.ia.864.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '864.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567247
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dg1', '288.dl1', '432.eu1', '432.r1', '432.fq1', '432.fs1', '432.fw1', '432.gc1', '432.gj1'], 'contains': ['1728.d1', '1728.o1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 87178324129, 36933], 'label': '6912.ia.864.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567248
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.df1', '432.ev1', '432.p1', '432.fq1', '432.fr1', '432.fy1', '432.gb1', '432.gj1'], 'contains': ['1728.d1', '1728.n1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 36933, 87100665], 'label': '6912.ia.864.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '864.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567249
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dh1', '432.ev1', '432.r1', '432.fp1', '432.ft1', '432.fv1', '432.gd1', '432.gj1'], 'contains': ['1728.d1', '1728.q1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7620480, 36933, 87265415329], 'label': '6912.ia.864.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567250
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dm1', '288.dq1', '432.b1', '432.t1', '432.fn1', '432.gk1', '432.gl1', '432.gm1', '432.gn1'], 'contains': ['1728.e1', '1728.f1', '1728.k1', '1728.cc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 36933, 746], 'label': '6912.ia.864.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567251
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '12.ca1', '12.cp1', '12.ct1', '12.cu1', '12.cv1', '12.cw1'], 'contains': ['48.bx1', '48.cm1', '72.ko1', '72.kr1', '96.ct1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.24.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567252
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dn1', '288.dr1', '432.b1', '432.v1', '432.fo1', '432.gk1', '432.go1', '432.gp1', '432.gq1'], 'contains': ['1728.e1', '1728.h1', '1728.i1', '1728.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218570880, 40280426, 36933], 'label': '6912.ia.864.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567253
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.do1', '288.ds1', '432.c1', '432.t1', '432.v1', '432.gl1', '432.gp1', '432.gr1', '432.gs1'], 'contains': ['1728.e1', '1728.h1', '1728.k1', '1728.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87218570880, 36933, 87096887], 'label': '6912.ia.864.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ex1', 'old_label': '864.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567254
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dp1', '288.dt1', '432.d1', '432.fn1', '432.fo1', '432.gm1', '432.go1', '432.gt1', '432.gu1'], 'contains': ['1728.e1', '1728.j1', '1728.l1', '1728.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 83468087, 87265382400], 'label': '6912.ia.864.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567255
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.du1', '432.e1', '432.y1', '432.fp1', '432.gn1', '432.gq1', '432.gr1', '432.gt1', '432.gv1', '432.gw1', '432.gx1', '432.gy1', '432.gz1', '432.ha1', '432.hb1', '432.hc1'], 'contains': ['1728.e1', '1728.m1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87305662080, 32929, 36933], 'label': '6912.ia.864.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567256
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dv1', '432.e1', '432.z1', '432.fq1', '432.gk1', '432.gs1', '432.gu1', '432.gv1', '432.hd1', '432.he1', '432.hf1'], 'contains': ['1728.e1', '1728.o1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87178324129, 127403809, 36933], 'label': '6912.ia.864.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567257
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fa1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dw1', '432.g1', '432.y1', '432.z1', '432.gl1', '432.gp1', '432.gw1', '432.hf1'], 'contains': ['1728.e1', '1728.n1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218603809, 127403809, 36933], 'label': '6912.ia.864.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.u1', 'old_label': '864.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567258
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dx1', '432.h1', '432.fp1', '432.fq1', '432.gm1', '432.go1', '432.gx1', '432.hd1'], 'contains': ['1728.e1', '1728.p1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 83495329, 87265382400], 'label': '6912.ia.864.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567259
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dy1', '288.dz1', '288.ea1', '288.en1', '432.es1', '432.bc1', '432.fn1', '432.hg1', '432.hh1', '432.hi1', '432.hj1'], 'contains': ['1728.f1', '1728.g1', '1728.l1', '1728.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426], 'label': '6912.ia.864.bw1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567260
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.eb1', '432.ew1', '432.bl1', '432.bm1', '432.fr1', '432.gk1', '432.gl1', '432.hg1'], 'contains': ['1728.f1', '1728.h1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36239, 36933, 87100665], 'label': '6912.ia.864.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '864.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567261
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ec1', '288.ed1', '432.ey1', '432.bd1', '432.fs1', '432.gk1', '432.hh1'], 'contains': ['1728.f1', '1728.i1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 746, 87178300665], 'label': '6912.ia.864.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '864.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567262
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '12.by1', '12.cf1'], 'contains': ['48.cc1', '48.cg1', '48.cn1', '72.ks1', '72.ku1', '96.cu1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.24.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '24.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567263
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ee1', '288.ef1', '432.ex1', '432.be1', '432.fr1', '432.fu1', '432.gm1', '432.hh1', '432.hi1'], 'contains': ['1728.f1', '1728.j1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7621226, 36933, 7629945], 'label': '6912.ia.864.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '864.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567264
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.eg1', '432.ew1', '432.bd1', '432.bf1', '432.ft1', '432.gl1', '432.gn1', '432.hi1'], 'contains': ['1728.f1', '1728.k1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 746, 87218580345], 'label': '6912.ia.864.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567265
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.eh1', '288.ei1', '288.ej1', '432.ex1', '432.bg1', '432.fs1', '432.ft1', '432.gm1', '432.hg1', '432.hj1'], 'contains': ['1728.f1', '1728.l1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87185912426, 87185921145], 'label': '6912.ia.864.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567266
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ek1', '288.el1', '288.em1', '432.ey1', '432.bm1', '432.fu1', '432.gn1', '432.hj1', '432.hl1', '432.hk1', '432.hm1', '432.hn1', '432.ho1', '432.hp1'], 'contains': ['1728.f1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 36933, 746], 'label': '6912.ia.864.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '864.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567267
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.eo1', '288.er1', '432.et1', '432.bc1', '432.fo1', '432.hg1', '432.hq1', '432.hr1', '432.hs1'], 'contains': ['1728.g1', '1728.h1', '1728.l1', '1728.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185911680, 36933, 87261759287], 'label': '6912.ia.864.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567268
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ep1', '288.es1', '288.et1', '432.es1', '432.bo1', '432.fo1', '432.hh1', '432.hq1', '432.ht1', '432.hu1'], 'contains': ['1728.g1', '1728.i1', '1728.j1', '1728.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185911680, 7621226, 36933], 'label': '6912.ia.864.ce1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567269
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.eq1', '288.eu1', '432.et1', '432.bo1', '432.fn1', '432.hi1', '432.hr1', '432.ht1', '432.hv1'], 'contains': ['1728.g1', '1728.j1', '1728.k1', '1728.cj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87185911680, 36933, 83468087], 'label': '6912.ia.864.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567270
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ev1', '288.ez1', '288.fb1', '432.eu1', '432.bq1', '432.fp1', '432.hj1', '432.hs1', '432.hu1', '432.hv1', '432.hx1', '432.hw1', '432.hy1', '432.hz1', '432.ia1', '432.ib1', '432.ic1', '432.id1'], 'contains': ['1728.g1', '1728.m1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 32929, 36933], 'label': '6912.ia.864.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567271
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ex1', '288.fa1', '432.eu1', '432.bs1', '432.fq1', '432.hh1', '432.hr1', '432.hx1', '432.ie1'], 'contains': ['1728.g1', '1728.o1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178324129, 36933, 83495329], 'label': '6912.ia.864.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ci1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567272
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ew1', '432.ev1', '432.bq1', '432.fq1', '432.hg1', '432.ht1', '432.hw1', '432.ie1'], 'contains': ['1728.g1', '1728.n1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185911680, 36933, 87100665], 'label': '6912.ia.864.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ch1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567273
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '12.bz1', '12.cp1', '12.da1', '12.db1', '12.dc1', '12.dd1'], 'contains': ['48.cc1', '48.cm1', '72.kt1', '72.kv1', '96.cv1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243567274
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ey1', '432.ev1', '432.bs1', '432.fp1', '432.hi1', '432.hq1', '432.hy1', '432.ie1'], 'contains': ['1728.g1', '1728.p1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 83495329, 87265415329], 'label': '6912.ia.864.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567275
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fc1', '432.ew1', '432.bd1', '432.bu1', '432.fv1', '432.gp1', '432.gq1', '432.hq1'], 'contains': ['1728.h1', '1728.i1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 36933, 87218580345], 'label': '6912.ia.864.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ck1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567276
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fd1', '432.ez1', '432.be1', '432.fr1', '432.fx1', '432.go1', '432.hq1', '432.hr1'], 'contains': ['1728.h1', '1728.j1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36933, 7629945, 83468087], 'label': '6912.ia.864.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '864.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567277
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fe1', '432.fa1', '432.bd1', '432.bx1', '432.fw1', '432.gk1', '432.gs1', '432.hr1'], 'contains': ['1728.h1', '1728.k1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40280426, 36933, 87178300665], 'label': '6912.ia.864.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567278
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ff1', '432.fb1', '432.bf1', '432.bu1', '432.bx1', '432.gl1', '432.gp1', '432.gr1'], 'contains': ['1728.h1', '1728.k1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87218580345, 87096887], 'label': '6912.ia.864.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ex1', 'old_label': '864.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567279
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fg1', '432.ez1', '432.bg1', '432.fv1', '432.fw1', '432.go1', '432.hg1', '432.hs1'], 'contains': ['1728.h1', '1728.l1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87261759287, 87185921145], 'label': '6912.ia.864.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.co1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567280
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fh1', '432.fa1', '432.bm1', '432.cc1', '432.fx1', '432.gq1', '432.gr1', '432.hs1', '432.ih1', '432.if1', '432.ig1', '432.ii1', '432.ij1', '432.ik1', '432.il1', '432.im1'], 'contains': ['1728.h1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 40280426, 36933], 'label': '6912.ia.864.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567281
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fi1', '432.fb1', '432.bl1', '432.cc1', '432.gp1', '432.gs1', '432.in1', '432.io1'], 'contains': ['1728.h1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40280426, 36933, 87100665], 'label': '6912.ia.864.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bm1', 'old_label': '864.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cq1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567282
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fj1', '288.fm1', '432.ex1', '432.cd1', '432.fs1', '432.fv1', '432.go1', '432.ht1', '432.hu1'], 'contains': ['1728.i1', '1728.j1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7621226, 36933, 87185921145], 'label': '6912.ia.864.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567283
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fn1', '432.ew1', '432.cj1', '432.ck1', '432.fy1', '432.gk1', '432.gp1', '432.ht1'], 'contains': ['1728.i1', '1728.k1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87178327439, 36933, 87100665], 'label': '6912.ia.864.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '864.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567284
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '12.ca1', '12.cg1', '12.dg1', '12.dh1', '12.di1', '12.dj1'], 'contains': ['48.cg1', '48.cm1', '72.kw1', '72.kx1', '72.ky1', '96.cw1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.24.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567285
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fk1', '288.fo1', '432.ex1', '432.ce1', '432.fy1', '432.fz1', '432.go1', '432.hh1', '432.hq1'], 'contains': ['1728.i1', '1728.l1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87185912426, 7629945], 'label': '6912.ia.864.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567366
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ls1', '288.lt1', '432.cl1', '432.kl1', '432.kh1', '432.kp1', '432.kw1'], 'contains': ['1728.bq1', '1728.br1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87222236613, 87091200, 83468087], 'label': '6912.ia.864.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567286
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fl1', '288.fp1', '432.ey1', '432.ck1', '432.fz1', '432.gq1', '432.hu1', '432.iq1', '432.ip1', '432.ir1', '432.is1', '432.it1', '432.iu1'], 'contains': ['1728.i1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87178291946], 'label': '6912.ia.864.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cu1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567287
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fq1', '432.ez1', '432.cd1', '432.ft1', '432.fw1', '432.gm1', '432.ht1', '432.hv1'], 'contains': ['1728.j1', '1728.k1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87185921145, 83468087], 'label': '6912.ia.864.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567288
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fr1', '288.fv1', '432.fc1', '432.cn1', '432.fs1', '432.fw1', '432.gu1', '432.hh1', '432.hr1'], 'contains': ['1728.j1', '1728.l1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 83468087, 87178300665], 'label': '6912.ia.864.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567289
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fs1', '432.fd1', '432.cn1', '432.ft1', '432.fv1', '432.gt1', '432.hi1', '432.hq1'], 'contains': ['1728.j1', '1728.l1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87265391865, 36933, 83468087], 'label': '6912.ia.864.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567290
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ft1', '288.fw1', '432.fc1', '432.cq1', '432.fu1', '432.fx1', '432.gt1', '432.hu1', '432.hv1', '432.iw1', '432.iv1', '432.ix1', '432.iy1', '432.iz1', '432.ja1', '432.jb1', '432.jc1'], 'contains': ['1728.j1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 36933, 83498639], 'label': '6912.ia.864.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '864.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cy1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567291
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fu1', '432.fd1', '432.cq1', '432.fr1', '432.gu1', '432.ht1', '432.jd1', '432.je1'], 'contains': ['1728.j1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7656719, 36933, 87100665], 'label': '6912.ia.864.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cz1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567292
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fx1', '432.ez1', '432.ce1', '432.fy1', '432.ga1', '432.gm1', '432.hi1', '432.hr1'], 'contains': ['1728.k1', '1728.l1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87261759287, 7629945], 'label': '6912.ia.864.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '864.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.da1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567293
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fy1', '432.fa1', '432.ck1', '432.cv1', '432.ga1', '432.gn1', '432.gr1', '432.hv1', '432.jh1', '432.jf1', '432.jg1', '432.ji1', '432.jj1', '432.jk1', '432.jl1', '432.jm1'], 'contains': ['1728.k1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 87218571626, 36933], 'label': '6912.ia.864.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.db1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567294
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.fz1', '432.fb1', '432.cj1', '432.cv1', '432.gl1', '432.gs1', '432.jn1', '432.jo1'], 'contains': ['1728.k1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218571626, 36933, 87100665], 'label': '6912.ia.864.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.t1', 'old_label': '864.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dc1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567295
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.cb1', '12.ch1', '12.cq1', '12.ct1', '12.da1', '12.dg1'], 'contains': ['48.cm1', '48.cn1', '72.kz1', '72.lh1', '96.cx1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.24.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567296
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ga1', '288.gc1', '288.gd1', '432.fc1', '432.cy1', '432.fz1', '432.ga1', '432.gt1', '432.hj1', '432.hs1', '432.jq1', '432.jp1', '432.jr1', '432.js1', '432.jt1', '432.ju1', '432.jv1', '432.jw1'], 'contains': ['1728.l1', '1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87261789839], 'label': '6912.ia.864.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dd1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567297
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gb1', '432.fd1', '432.cy1', '432.fy1', '432.gu1', '432.hg1', '432.jx1', '432.jy1'], 'contains': ['1728.l1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185947919, 36933, 87100665], 'label': '6912.ia.864.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '864.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.de1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567298
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gf1', '288.gy1', '432.fj1', '432.da1', '432.gc1', '432.gv1', '432.hl1', '432.hx1', '432.ih1', '432.iq1', '432.iw1', '432.jh1', '432.jq1'], 'contains': ['1728.m1', '1728.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 36933, 87178300665], 'label': '6912.ia.864.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dg1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567299
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ge1', '432.fe1', '432.dr1', '432.ds1', '432.gb1', '432.gv1', '432.gw1', '432.hk1', '432.hw1', '432.if1', '432.ig1', '432.ip1', '432.iv1', '432.jf1', '432.jg1', '432.jp1'], 'contains': ['1728.m1', '1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87100665, 87124129], 'label': '6912.ia.864.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.df1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567300
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gg1', '288.gz1', '432.ff1', '432.dc1', '432.gb1', '432.gi1', '432.gx1', '432.hm1', '432.hx1', '432.hy1', '432.ii1', '432.ir1', '432.ix1', '432.iy1', '432.ji1', '432.jr1', '432.js1'], 'contains': ['1728.m1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [32929, 36933, 83480268], 'label': '6912.ia.864.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '864.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dh1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567301
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gh1', '432.fe1', '432.da1', '432.de1', '432.gd1', '432.gw1', '432.hc1', '432.hn1', '432.hy1', '432.ij1', '432.ik1', '432.is1', '432.iz1', '432.jj1', '432.jk1', '432.jt1'], 'contains': ['1728.m1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [32929, 36933, 87265400268], 'label': '6912.ia.864.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.di1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567302
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gi1', '288.ha1', '288.hi1', '432.ff1', '432.dg1', '432.gc1', '432.gd1', '432.gx1', '432.ho1', '432.hw1', '432.id1', '432.il1', '432.it1', '432.ja1', '432.jb1', '432.jl1', '432.ju1', '432.jv1'], 'contains': ['1728.m1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [32929, 36933, 87261771468], 'label': '6912.ia.864.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dj1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567303
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gj1', '288.hb1', '288.hj1', '432.fg1', '432.dj1', '432.ge1', '432.gy1', '432.hp1', '432.hz1', '432.if1', '432.iq1', '432.ix1', '432.jj1', '432.ju1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 34210, 36933], 'label': '6912.ia.864.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '864.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567304
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gk1', '432.fh1', '432.dj1', '432.dk1', '432.gf1', '432.gz1', '432.ha1', '432.hk1', '432.ia1', '432.ig1', '432.im1', '432.is1', '432.iy1', '432.jh1', '432.jk1', '432.jv1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 40313890, 36933], 'label': '6912.ia.864.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '864.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567305
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gl1', '288.hc1', '432.fg1', '432.dl1', '432.gg1', '432.gz1', '432.hl1', '432.ib1', '432.ij1', '432.iu1', '432.ja1', '432.jf1', '432.jr1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 36933, 87178325410], 'label': '6912.ia.864.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567306
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.bt1', '12.ci1', '12.cq1', '12.cu1', '12.db1', '12.dh1'], 'contains': ['48.cm1', '48.co1', '72.la1', '72.li1', '96.cy1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.24.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243567307
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gm1', '288.hd1', '432.fi1', '432.dm1', '432.ge1', '432.gf1', '432.hb1', '432.hm1', '432.ib1', '432.ic1', '432.ii1', '432.it1', '432.iv1', '432.jc1', '432.jl1', '432.jq1', '432.jt1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 7654690, 36933], 'label': '6912.ia.864.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '864.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567308
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gn1', '432.fh1', '432.dl1', '432.do1', '432.gh1', '432.gy1', '432.ha1', '432.hn1', '432.ic1', '432.ih1', '432.ik1', '432.ip1', '432.jb1', '432.jg1', '432.jm1', '432.js1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [9465, 36933, 87218605090], 'label': '6912.ia.864.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.do1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567309
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.go1', '288.he1', '288.hk1', '432.fi1', '432.dp1', '432.gg1', '432.gh1', '432.hb1', '432.ho1', '432.hz1', '432.ia1', '432.il1', '432.ir1', '432.iw1', '432.iz1', '432.ji1', '432.jp1', '432.jw1'], 'contains': ['1728.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [9465, 36933, 87185945890], 'label': '6912.ia.864.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '864.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567310
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gp1', '432.fe1', '432.da1', '432.dw1', '432.gj1', '432.gv1', '432.hf1', '432.ie1'], 'contains': ['1728.o1', '1728.n1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127403809, 36933, 87305671545], 'label': '6912.ia.864.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.s1', 'old_label': '864.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567311
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gw1', '288.hg1', '432.ff1', '432.eb1', '432.gc1', '432.gj1', '432.hd1', '432.hx1', '432.ie1'], 'contains': ['1728.o1', '1728.p1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87178324129, 36933, 83480268], 'label': '6912.ia.864.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '864.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567312
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gq1', '432.fk1', '432.dc1', '432.gb1', '432.hd1', '432.ie1', '432.in1', '432.jn1'], 'contains': ['1728.n1', '1728.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7653409, 36933, 87100665], 'label': '6912.ia.864.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '864.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dr1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567313
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gr1', '432.fm1', '432.de1', '432.dw1', '432.gw1', '432.hf1', '432.jd1', '432.jx1'], 'contains': ['1728.n1', '1728.q1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [127403809, 36933, 87265400268], 'label': '6912.ia.864.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.w1', 'old_label': '864.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ds1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567314
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gs1', '432.fk1', '432.dg1', '432.gj1', '432.hd1', '432.hw1', '432.io1', '432.jo1'], 'contains': ['1728.n1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87185944609, 36933, 87100665], 'label': '6912.ia.864.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '864.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dt1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 243567315
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gt1', '432.fl1', '432.dn1', '432.he1', '432.in1', '432.je1', '432.jo1', '432.jx1'], 'contains': ['1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43942690, 36933, 87100665], 'label': '6912.ia.864.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '864.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.du1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567316
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gu1', '432.fl1', '432.dq1', '432.he1', '432.io1', '432.jd1', '432.jn1', '432.jy1'], 'contains': ['1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87222233890, 87100665], 'label': '6912.ia.864.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567317
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.bt1', '12.cb1', '12.cj1', '12.cv1', '12.dc1', '12.di1'], 'contains': ['48.cm1', '48.cp1', '72.lb1', '72.lj1', '72.lq1', '96.cz1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.24.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567318
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gv1', '288.hn1', '288.hp1', '432.fm1', '432.dr1', '432.hf1', '432.je1', '432.jy1'], 'contains': ['1728.n1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127388748, 36933, 87124129], 'label': '6912.ia.864.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '864.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567319
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.gx1', '432.fk1', '432.eb1', '432.gd1', '432.gj1', '432.gx1', '432.hy1', '432.ie1'], 'contains': ['1728.p1', '1728.q1', '1728.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 83480268, 87265415329], 'label': '6912.ia.864.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '864.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567320
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.iq1', '288.ir1', '432.eh1', '432.kb1', '432.kc1', '432.kd1'], 'contains': ['1728.bf1', '1728.s1', '1728.be1', '1728.bl1', '1728.u1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40316613, 127370880, 87178291200], 'label': '6912.ia.864.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.dz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567321
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.jh1', '288.jt1', '432.a1', '432.kb1', '432.ki1', '432.kj1', '432.km1'], 'contains': ['1728.bf1', '1728.bg1', '1728.bk1', '1728.bn1', '1728.bx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7657413, 87178328133, 87091200], 'label': '6912.ia.864.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.ea1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ev1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567322
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ji1', '288.ju1', '432.b1', '432.kc1', '432.ki1', '432.kk1', '432.kn1'], 'contains': ['1728.bf1', '1728.bh1', '1728.bi1', '1728.bm1', '1728.bp1', '1728.cc1', '1728.cd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40280426, 87178328133, 40279680], 'label': '6912.ia.864.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.eb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ew1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567323
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.jj1', '288.jv1', '432.c1', '432.kc1', '432.kj1', '432.kl1', '432.kn1'], 'contains': ['1728.bf1', '1728.bi1', '1728.bo1', '1728.br1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87178328133, 87096887, 40279680], 'label': '6912.ia.864.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ec1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ex1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567324
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.jk1', '288.jw1', '432.d1', '432.kd1', '432.ki1', '432.kl1', '432.ko1'], 'contains': ['1728.bf1', '1728.bj1', '1728.bq1', '1728.bs1', '1728.cf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87178328133, 87091200, 83468087], 'label': '6912.ia.864.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ed1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ey1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567325
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.jl1', '288.jx1', '432.f1', '432.kb1', '432.kk1', '432.kl1', '432.km1'], 'contains': ['1728.bf1', '1728.bt1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43908480, 87178328133, 87091200], 'label': '6912.ia.864.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.ee1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ez1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567326
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.jm1', '288.jy1', '432.j1', '432.kd1', '432.kj1', '432.kk1', '432.ko1'], 'contains': ['1728.bf1', '1728.bv1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [43944719, 87178328133, 87091200], 'label': '6912.ia.864.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ef1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fa1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567327
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.e1', '288.jn1', '288.jo1', '288.jp1', '432.eh1', '432.km1', '432.kn1', '432.ko1'], 'contains': ['1728.a1', '1728.bf1', '1728.bl1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 87178328133, 40279680], 'label': '6912.ia.864.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.eg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567328
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '12.cc1', '12.ck1', '12.cr1', '12.ct1', '12.db1', '12.di1'], 'contains': ['48.cm1', '72.lc1', '72.lk1', '72.lr1', '96.da1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567329
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.hq1', '288.hu1', '432.a1', '432.jz1'], 'contains': ['1728.s1', '1728.bg1', '1728.t1', '1728.w1', '1728.bx1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87128133, 87178328133], 'label': '6912.ia.864.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.eh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567330
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.hr1', '288.hv1', '432.b1', '432.kc1', '432.jz1'], 'contains': ['1728.s1', '1728.bh1', '1728.bi1', '1728.v1', '1728.y1', '1728.cc1', '1728.cd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 40280426, 87178328133], 'label': '6912.ia.864.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ei1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ea1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567331
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.hs1', '288.hw1', '432.c1', '432.kc1', '432.ka1'], 'contains': ['1728.s1', '1728.bi1', '1728.x1', '1728.ba1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87178328133, 87096887], 'label': '6912.ia.864.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ew1', 'old_label': '864.ej1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567332
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ht1', '288.hx1', '432.d1', '432.jz1', '432.ka1'], 'contains': ['1728.s1', '1728.bj1', '1728.z1', '1728.bb1', '1728.cf1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87128133, 87178328133, 83468087], 'label': '6912.ia.864.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '864.ek1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ec1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567333
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.hy1', '432.i1', '432.ka1'], 'contains': ['1728.s1', '1728.bc1', '1728.bd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87128133, 43931924, 87178328133], 'label': '6912.ia.864.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.el1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ed1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567334
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.jq1', '288.js1', '288.jz1', '432.es1', '432.ki1', '432.jz1'], 'contains': ['1728.bg1', '1728.bh1', '1728.bj1', '1728.by1', '1728.ca1', '1728.cg1', '1728.ci1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7657413, 7621226, 87178328133], 'label': '6912.ia.864.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.em1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567335
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.jr1', '288.ka1', '432.et1', '432.ki1', '432.jz1'], 'contains': ['1728.bg1', '1728.bi1', '1728.bj1', '1728.bz1', '1728.cb1', '1728.ch1', '1728.cj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7657413, 87178328133, 83468087], 'label': '6912.ia.864.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.en1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567336
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.is1', '288.it1', '288.iu1', '432.ei1', '432.kb1', '432.ke1', '432.kf1'], 'contains': ['1728.be1', '1728.bk1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40316613, 7657413, 127407813], 'label': '6912.ia.864.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.eo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ep1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567337
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.iv1', '288.iw1', '432.ej1', '432.kc1', '432.ke1', '432.kg1'], 'contains': ['1728.be1', '1728.bm1', '1728.bo1', '1728.v1', '1728.x1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 127370880, 40280426], 'label': '6912.ia.864.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.ep1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567338
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ix1', '288.iy1', '432.ek1', '432.kb1', '432.kg1', '432.kh1'], 'contains': ['1728.be1', '1728.bn1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40316613, 87185948613, 127407813], 'label': '6912.ia.864.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.eq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.er1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567339
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.c1'], 'contains': ['12.b1', '12.br1', '12.bu1', '12.ch1', '12.ck1', '12.ct1', '12.cw1', '18.bd1', '18.bn1', '24.di1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.s1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567340
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '12.cd1', '12.ch1', '12.cs1', '12.cw1', '12.dc1', '12.dh1'], 'contains': ['48.cm1', '72.ld1', '72.ll1', '96.db1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87305681228, 127370880, 127380345, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.24.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567341
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.iz1', '288.ja1', '288.jb1', '432.el1', '432.kc1', '432.kf1', '432.kh1'], 'contains': ['1728.be1', '1728.bp1', '1728.br1', '1728.y1', '1728.ba1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40316613, 127370880, 87218571626], 'label': '6912.ia.864.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.er1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.es1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567342
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.jc1', '288.jd1', '432.em1', '432.kd1', '432.ke1', '432.kh1'], 'contains': ['1728.be1', '1728.bq1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 43944719, 127407813], 'label': '6912.ia.864.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.es1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.et1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567343
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.je1', '288.jf1', '288.jg1', '432.en1', '432.kd1', '432.kf1', '432.kg1'], 'contains': ['1728.be1', '1728.bs1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40316613, 87222235919, 127407813], 'label': '6912.ia.864.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.et1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567344
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.kb1', '288.kc1', '432.k1', '432.kb1', '432.km1', '432.kp1', '432.kq1'], 'contains': ['1728.bk1', '1728.bl1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87218607813, 87091200], 'label': '6912.ia.864.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.eu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fe1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567345
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kd1', '288.ke1', '432.l1', '432.ki1', '432.ke1', '432.kp1', '432.kt1'], 'contains': ['1728.bk1', '1728.bm1', '1728.bq1', '1728.by1', '1728.bz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7657413, 87091200, 83468087], 'label': '6912.ia.864.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.ev1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ff1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567346
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kf1', '288.kg1', '432.m1', '432.kj1', '432.ke1', '432.kq1', '432.kt1'], 'contains': ['1728.bk1', '1728.bo1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 7657413, 87091200], 'label': '6912.ia.864.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.ew1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567347
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kh1', '288.ki1', '288.kj1', '432.n1', '432.ki1', '432.kf1', '432.kq1', '432.ku1'], 'contains': ['1728.bk1', '1728.bp1', '1728.bs1', '1728.ca1', '1728.cb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7657413, 87261759287, 87091200], 'label': '6912.ia.864.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ex1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567348
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kk1', '288.kl1', '288.km1', '432.o1', '432.kj1', '432.kf1', '432.kp1', '432.ku1'], 'contains': ['1728.bk1', '1728.br1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7657413, 87222200426, 87091200], 'label': '6912.ia.864.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ey1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567349
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kn1', '288.ks1', '432.t1', '432.kc1', '432.kn1', '432.kp1', '432.kr1'], 'contains': ['1728.bl1', '1728.bm1', '1728.br1', '1728.cc1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40280426, 87305699013, 40279680], 'label': '6912.ia.864.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.ez1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567350
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.ko1', '288.kt1', '432.u1', '432.kb1', '432.km1', '432.kr1', '432.ks1'], 'contains': ['1728.bl1', '1728.bn1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87218607813, 43908480, 87091200], 'label': '6912.ia.864.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.fa1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567351
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '12.cc1', '12.ci1', '12.cs1', '12.cv1', '12.dd1', '12.dg1'], 'contains': ['48.cm1', '72.le1', '72.lm1', '96.dc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.24.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567352
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kp1', '288.ku1', '432.v1', '432.kc1', '432.kn1', '432.kq1', '432.ks1'], 'contains': ['1728.bl1', '1728.bo1', '1728.bp1', '1728.cd1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87096887, 87305699013, 40279680], 'label': '6912.ia.864.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567353
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kq1', '288.kv1', '432.w1', '432.kd1', '432.ko1', '432.kp1', '432.ks1'], 'contains': ['1728.bl1', '1728.bq1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87218607813, 83476887, 87091200], 'label': '6912.ia.864.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567354
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kr1', '288.kw1', '432.x1', '432.kd1', '432.ko1', '432.kq1', '432.kr1'], 'contains': ['1728.bl1', '1728.bs1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87218570880, 43909226, 87091200], 'label': '6912.ia.864.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567355
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kx1', '288.la1', '432.bc1', '432.ki1', '432.kg1', '432.kr1', '432.kv1'], 'contains': ['1728.bm1', '1728.bn1', '1728.bs1', '1728.cg1', '1728.ch1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87185948613, 87261759287, 87091200], 'label': '6912.ia.864.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fe1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567356
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ky1', '288.lb1', '432.bh1', '432.kk1', '432.ke1', '432.kr1', '432.kt1'], 'contains': ['1728.bm1', '1728.bt1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43909226, 43945413, 87091200], 'label': '6912.ia.864.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.ff1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567357
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.kz1', '288.lc1', '432.bi1', '432.kk1', '432.kg1', '432.kp1', '432.kv1'], 'contains': ['1728.bm1', '1728.bu1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87222200426, 87222236613, 87091200], 'label': '6912.ia.864.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567358
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ld1', '288.lg1', '432.bn1', '432.kj1', '432.kg1', '432.ks1', '432.kv1'], 'contains': ['1728.bn1', '1728.bo1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87222200426, 87185948613, 87091200], 'label': '6912.ia.864.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567359
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.le1', '288.lh1', '432.bo1', '432.ki1', '432.kh1', '432.ks1', '432.kw1'], 'contains': ['1728.bn1', '1728.bp1', '1728.bq1', '1728.ci1', '1728.cj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87185948613, 87091200, 83468087], 'label': '6912.ia.864.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567360
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.lf1', '288.li1', '432.bp1', '432.kj1', '432.kh1', '432.kr1', '432.kw1'], 'contains': ['1728.bn1', '1728.br1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [43909226, 87185948613, 87091200], 'label': '6912.ia.864.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ft1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567361
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.lj1', '288.ll1', '432.bv1', '432.kl1', '432.ke1', '432.ks1', '432.kt1'], 'contains': ['1728.bo1', '1728.bq1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [43908480, 87091200, 83468087], 'label': '6912.ia.864.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.fk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567362
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '12.cd1', '12.cj1', '12.cr1', '12.cu1', '12.da1', '12.dj1'], 'contains': ['48.cm1', '72.lf1', '72.ln1', '72.ls1', '96.dd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.24.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '24.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567363
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.lk1', '288.lm1', '432.by1', '432.kl1', '432.kg1', '432.kq1', '432.kv1'], 'contains': ['1728.bo1', '1728.bs1', '1728.bu1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87222236613, 87261759287, 87091200], 'label': '6912.ia.864.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567364
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ln1', '288.lp1', '288.lr1', '432.cf1', '432.kk1', '432.kf1', '432.ks1', '432.ku1'], 'contains': ['1728.bp1', '1728.bt1', '1728.bw1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [43908480, 87222200426, 87091200], 'label': '6912.ia.864.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567365
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.lo1', '288.lq1', '432.cg1', '432.kk1', '432.kh1', '432.kq1', '432.kw1'], 'contains': ['1728.bp1', '1728.bu1', '1728.bv1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [43909226, 87222236613, 87091200], 'label': '6912.ia.864.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567367
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.lu1', '288.lv1', '288.lw1', '432.cr1', '432.kl1', '432.kf1', '432.kr1', '432.ku1'], 'contains': ['1728.br1', '1728.bs1', '1728.bt1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [43945413, 87261759287, 87091200], 'label': '6912.ia.864.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567368
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.f1', '288.lx1', '288.ly1', '288.lz1', '432.ei1', '432.km1', '432.kt1', '432.ku1'], 'contains': ['1728.a1', '1728.bk1', '1728.bt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 7657413, 40279680], 'label': '6912.ia.864.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.fq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ga1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567369
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ma1', '288.mb1', '288.mc1', '288.md1', '432.ej1', '432.kn1', '432.kt1', '432.kv1'], 'contains': ['1728.a1', '1728.bm1', '1728.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 40280426, 40279680], 'label': '6912.ia.864.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '864.fr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567370
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.me1', '288.mf1', '288.mg1', '288.mh1', '432.ek1', '432.km1', '432.kv1', '432.kw1'], 'contains': ['1728.a1', '1728.bn1', '1728.bu1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 87185948613, 40279680], 'label': '6912.ia.864.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.fs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567371
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mi1', '288.mj1', '288.mk1', '288.ml1', '432.el1', '432.kn1', '432.ku1', '432.kw1'], 'contains': ['1728.a1', '1728.bp1', '1728.br1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 87218571626, 40279680], 'label': '6912.ia.864.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '864.ft1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567372
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mm1', '288.mn1', '288.mo1', '288.mp1', '432.em1', '432.ko1', '432.kt1', '432.kw1'], 'contains': ['1728.a1', '1728.bq1', '1728.bv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 43909226, 40279680], 'label': '6912.ia.864.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '864.fu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ge1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567373
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '12.cb1', '12.cq1'], 'contains': ['48.cn1', '48.co1', '48.cp1', '72.lg1', '72.lo1', '96.df1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 87218603809, 93405312000, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.24.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567374
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mq1', '288.mr1', '288.ms1', '288.mt1', '288.mu1', '288.mv1', '288.mw1', '432.en1', '432.ko1', '432.ku1', '432.kv1'], 'contains': ['1728.a1', '1728.bs1', '1728.bw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [127370880, 87222200426, 40279680], 'label': '6912.ia.864.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '864.fv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567375
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.hz1', '288.ia1', '432.l1', '432.jz1'], 'contains': ['1728.t1', '1728.v1', '1728.z1', '1728.by1', '1728.bz1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87128133, 83468087], 'label': '6912.ia.864.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '864.fw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ee1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567376
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ib1', '288.ic1', '288.id1', '432.n1', '432.jz1'], 'contains': ['1728.t1', '1728.y1', '1728.bb1', '1728.ca1', '1728.cb1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7620480, 87128133, 87261759287], 'label': '6912.ia.864.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.fx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ef1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567377
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ie1', '288.ig1', '432.t1', '432.kc1'], 'contains': ['1728.u1', '1728.v1', '1728.ba1', '1728.cc1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87305662080, 40280426], 'label': '6912.ia.864.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ho1', 'old_label': '864.fy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567378
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.if1', '288.ih1', '432.v1', '432.kc1'], 'contains': ['1728.u1', '1728.x1', '1728.y1', '1728.cd1', '1728.ce1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40316613, 87305662080, 87096887], 'label': '6912.ia.864.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ho1', 'old_label': '864.fz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567379
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ii1', '288.ij1', '432.bc1', '432.jz1'], 'contains': ['1728.v1', '1728.w1', '1728.bb1', '1728.cg1', '1728.ch1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87185911680, 87128133, 87261759287], 'label': '6912.ia.864.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.ga1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ei1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567380
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ik1', '288.il1', '432.bo1', '432.jz1'], 'contains': ['1728.w1', '1728.y1', '1728.z1', '1728.ci1', '1728.cj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87185911680, 87128133, 83468087], 'label': '6912.ia.864.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.gb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ej1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567381
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.im1', '432.bw1', '432.ka1'], 'contains': ['1728.x1', '1728.z1', '1728.bc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [119759865, 87128133, 83468087], 'label': '6912.ia.864.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.s1', 'old_label': '864.gc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ek1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567382
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.in1', '432.bz1', '432.ka1'], 'contains': ['1728.x1', '1728.bb1', '1728.bd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87298051065, 87128133, 87261759287], 'label': '6912.ia.864.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.l1', 'old_label': '864.gd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.el1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567383
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.io1', '432.cm1', '432.ka1'], 'contains': ['1728.z1', '1728.ba1', '1728.bd1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87298051065, 87128133, 83468087], 'label': '6912.ia.864.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.l1', 'old_label': '864.ge1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.em1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567384
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.bw1', '12.de1', '12.dk1'], 'contains': ['72.a1', '72.lu1', '72.lv1', '96.u1', '96.dg1', '96.dh1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.24.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1', 'subgroup_fusion': None, 'weyl_group': '576.8657'}
  • id: 243567385
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ip1', '432.cs1', '432.ka1'], 'contains': ['1728.ba1', '1728.bb1', '1728.bc1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [119759865, 87128133, 87261759287], 'label': '6912.ia.864.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.l1', 'old_label': '864.gf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.en1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 243567386
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.mx1', '288.mz1', '432.fn1', '432.ki1', '432.jz1'], 'contains': ['1728.bx1', '1728.by1', '1728.cb1', '1728.cc1', '1728.cf1', '1728.cg1', '1728.cj1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7620480, 7621226, 87265419333], 'label': '6912.ia.864.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.gg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567387
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '864.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.my1', '288.na1', '432.fo1', '432.ki1', '432.jz1'], 'contains': ['1728.bx1', '1728.bz1', '1728.ca1', '1728.cd1', '1728.cf1', '1728.ch1', '1728.ci1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [7657413, 87265419333, 83468087], 'label': '6912.ia.864.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '864.gh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567388
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['384.a1', '384.b1', '384.c1', '576.a1', '576.d1', '576.j1', '576.o1', '576.p1', '576.u1', '576.x1', '576.ba1', '576.bd1', '576.bh1', '576.bk1', '576.br1', '576.bt1', '576.bs1', '576.bu1', '576.bv1', '576.bw1'], 'contains': ['2304.a1', '3456.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93405312000, 36933], 'label': '6912.ia.1152.a1', 'mobius_quo': 1, 'mobius_sub': -1152, 'normal_closure': '1152.a1', 'normal_contained_in': ['288.a1', '288.c1', '576.a1'], 'normal_contains': ['2304.a1', '3456.a1'], 'normalizer': '1.a1', 'old_label': '1152.a1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '576.8653', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '1152.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567389
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1', 'complements': ['6.bk1', '6.c1', '6.bd1', '6.be1', '6.bi1', '6.bj1'], 'conjugacy_class_count': 2, 'contained_in': ['384.j1', '384.k1', '384.l1', '576.a1', '576.dp1', '576.ce1', '576.dq1', '576.dr1', '576.ds1', '576.dt1'], 'contains': ['2304.a1', '3456.c1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [93405312000, 87178291200], 'label': '6912.ia.1152.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '1152.b1', 'normal_contained_in': ['288.e1', '576.a1'], 'normal_contains': ['2304.a1'], 'normalizer': '1.a1', 'old_label': '1152.b1', 'projective_image': '6912.ia', 'quotient_action_image': '2.1', 'quotient_action_kernel': '576.8280', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '1152.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567390
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1', '384.a1', '384.d1', '384.e1', '576.g1', '576.e1', '576.k1', '576.n1', '576.s1', '576.t1', '576.y1', '576.bb1', '576.be1', '576.bi1', '576.bl1'], 'contains': ['2304.b1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [36933, 2676], 'label': '6912.ia.1152.c1', 'mobius_quo': None, 'mobius_sub': -288, 'normal_closure': '288.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '1152.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567391
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1', '384.b1', '384.d1', '384.f1', '576.h1', '576.m1', '576.q1', '576.v1', '576.z1', '576.bf1', '576.bm1', '576.bx1', '576.by1', '576.bz1', '576.ca1'], 'contains': ['2304.c1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [47537280, 36933], 'label': '6912.ia.1152.d1', 'mobius_quo': None, 'mobius_sub': -288, 'normal_closure': '288.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '1152.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567392
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.hh1', '384.a1', '384.f1', '384.g1', '576.f1', '576.l1', '576.bc1', '576.bj1', '576.bn1'], 'contains': ['2304.d1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36933, 93405314676], 'label': '6912.ia.1152.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '1152.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567393
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.by1', '384.b1', '384.e1', '384.g1', '576.r1', '576.w1', '576.bo1', '576.cb1', '576.cc1'], 'contains': ['2304.e1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93452849280, 36933], 'label': '6912.ia.1152.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '1152.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567394
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bz1', '288.hm1', '288.hn1', '384.c1', '384.d1', '384.g1', '576.i1', '576.bg1', '576.bp1'], 'contains': ['2304.f1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120116474, 36933], 'label': '6912.ia.1152.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '1152.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567395
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.cl1', '12.co1', '12.dm1'], 'contains': ['72.b1', '72.lt1', '72.lv1', '96.w1', '96.dj1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40312609, 36933, 87109068, 40279680], 'label': '6912.ia.24.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '24.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567396
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ca1', '288.ho1', '288.hp1', '384.c1', '384.e1', '384.f1', '384.g1', '576.bq1'], 'contains': ['2304.g1', '3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [93525428474, 36933], 'label': '6912.ia.1152.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.g1', 'old_label': '1152.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567397
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.i1', '384.j1', '576.g1', '576.dg1', '576.cd1', '576.dh1', '576.dk1', '576.dl1', '576.dm1'], 'contains': ['2304.b1', '3456.c1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87178328133, 2676], 'label': '6912.ia.1152.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '1152.i1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567398
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.db1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.jo1', '384.i1', '384.k1', '576.h1', '576.di1', '576.dj1', '576.dn1'], 'contains': ['2304.c1', '3456.c1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [47537280, 87178328133], 'label': '6912.ia.1152.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '1152.j1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567399
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.jp1', '384.i1', '384.l1', '576.i1', '576.do1'], 'contains': ['2304.f1', '3456.c1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [120116474, 87178328133], 'label': '6912.ia.1152.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bb1', 'old_label': '1152.k1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567400
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.m1', '576.b1', '576.d1', '576.dp1', '576.dd1', '576.du1', '576.dy1', '576.dz1', '576.ec1', '576.ed1', '576.ef1', '576.ei1', '576.ek1', '576.en1', '576.eq1', '576.er1', '576.es1', '576.et1'], 'contains': ['2304.a1', '3456.d1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [93405312000, 40279680], 'label': '6912.ia.1152.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '576.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1152.l1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567401
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.m1', '576.e1', '576.dg1', '576.de1', '576.dv1', '576.dx1', '576.ea1', '576.eb1', '576.ee1', '576.eg1', '576.ej1', '576.el1', '576.eo1', '576.eu1', '576.ev1', '576.ew1', '576.ex1', '576.fa1'], 'contains': ['2304.b1', '3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2676, 40279680], 'label': '6912.ia.1152.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '1152.m1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567402
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.m1', '576.f1', '576.df1', '576.dw1', '576.eh1', '576.em1', '576.ep1', '576.ey1', '576.ez1', '576.fb1'], 'contains': ['2304.d1', '3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405314676, 40279680], 'label': '6912.ia.1152.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '1152.n1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567403
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.h1', '576.d1', '576.ce1', '576.dd1', '576.cf1', '576.cj1', '576.ck1', '576.cn1', '576.co1', '576.cq1', '576.ct1', '576.cv1', '576.cy1', '576.db1', '576.dc1'], 'contains': ['2304.a1', '3456.b1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40316613, 93405312000], 'label': '6912.ia.1152.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1152.o1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567404
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.h1', '576.e1', '576.cd1', '576.de1', '576.cg1', '576.ci1', '576.cl1', '576.cm1', '576.cp1', '576.cr1', '576.cu1', '576.cw1', '576.cz1'], 'contains': ['2304.b1', '3456.b1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40316613, 2676], 'label': '6912.ia.1152.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '1152.p1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567405
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.h1', '576.f1', '576.df1', '576.ch1', '576.cs1', '576.cx1', '576.da1'], 'contains': ['2304.d1', '3456.b1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40316613, 93405314676], 'label': '6912.ia.1152.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bn1', 'old_label': '1152.q1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567406
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.ce1', '12.cy1', '12.dn1'], 'contains': ['72.c1', '72.lp1', '72.lv1', '96.x1', '96.dk1'], 'core': '72.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [93525427956, 127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.24.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '24.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567407
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.n1', '384.o1', '576.j1', '576.dq1', '576.du1', '576.cf1', '576.fg1', '576.fh1', '576.fj1', '576.fl1', '576.fo1'], 'contains': ['2304.a1', '3456.e1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000], 'label': '6912.ia.1152.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '1152.r1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567408
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.n1', '384.p1', '576.k1', '576.dh1', '576.dv1', '576.cg1', '576.ff1', '576.fi1', '576.fk1', '576.fm1', '576.fp1'], 'contains': ['2304.b1', '3456.e1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7657413, 2676], 'label': '6912.ia.1152.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '1152.s1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567409
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.n1', '384.q1', '576.l1', '576.dw1', '576.ch1', '576.fn1', '576.fq1'], 'contains': ['2304.d1', '3456.e1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7657413, 93405314676], 'label': '6912.ia.1152.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.q1', 'old_label': '1152.t1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567410
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.f1', '384.o1', '384.p1', '384.q1', '576.m1', '576.di1', '576.fr1', '576.fs1'], 'contains': ['2304.c1', '3456.e1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [7657413, 47537280], 'label': '6912.ia.1152.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '1152.u1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567411
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ir1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.r1', '576.n1', '576.dg1', '576.cd1', '576.dx1', '576.ci1', '576.ff1', '576.ft1', '576.fu1', '576.fv1', '576.fw1'], 'contains': ['2304.b1', '3456.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87218607813, 2676], 'label': '6912.ia.1152.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '1152.v1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567412
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.r1', '576.o1', '576.dp1', '576.ce1', '576.dy1', '576.cj1', '576.fg1', '576.fx1', '576.fy1', '576.fz1', '576.ga1'], 'contains': ['2304.a1', '3456.f1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87218570880, 93405312000], 'label': '6912.ia.1152.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1152.w1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567413
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.s1', '384.t1', '576.p1', '576.dr1', '576.dz1', '576.ck1', '576.fh1', '576.fx1', '576.gb1'], 'contains': ['2304.a1', '3456.g1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 746], 'label': '6912.ia.1152.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '1152.x1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567414
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mb1', '384.s1', '384.u1', '576.q1', '576.dj1', '576.fr1', '576.gc1'], 'contains': ['2304.c1', '3456.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [47537280, 746], 'label': '6912.ia.1152.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '1152.y1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567415
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mc1', '384.s1', '384.v1', '576.r1', '576.gd1'], 'contains': ['2304.e1', '3456.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93452849280, 746], 'label': '6912.ia.1152.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cc1', 'old_label': '1152.z1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567416
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.t1', '384.u1', '384.v1', '576.s1', '576.dk1', '576.ea1', '576.cl1', '576.fi1', '576.ft1', '576.ge1'], 'contains': ['2304.b1', '3456.g1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [36239, 2676], 'label': '6912.ia.1152.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '1152.ba1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567417
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.do1'], 'contains': ['72.lp1', '72.lt1', '72.lu1', '72.lv1', '96.y1', '96.dl1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.24.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '24.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 243567418
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.w1', '384.x1', '384.y1', '576.t1', '576.dh1', '576.eb1', '576.cm1', '576.ff1', '576.ge1', '576.gf1', '576.gg1', '576.gh1'], 'contains': ['2304.b1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [87185911680, 2676], 'label': '6912.ia.1152.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '1152.bb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567419
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.w1', '384.z1', '576.u1', '576.dq1', '576.ec1', '576.cn1', '576.fg1', '576.gb1', '576.gi1', '576.gk1', '576.gl1'], 'contains': ['2304.a1', '3456.h1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87185948613], 'label': '6912.ia.1152.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '1152.bc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567420
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.mg1', '384.x1', '384.z1', '576.v1', '576.di1', '576.gc1', '576.gj1'], 'contains': ['2304.c1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [47537280, 87185948613], 'label': '6912.ia.1152.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '1152.bd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567421
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.mh1', '384.y1', '384.z1', '576.w1', '576.gd1'], 'contains': ['2304.e1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87185948613, 93452849280], 'label': '6912.ia.1152.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '1152.be1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567422
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.ba1', '576.x1', '576.ds1', '576.dz1', '576.ed1', '576.ck1', '576.co1', '576.fj1', '576.fy1', '576.fz1', '576.gi1'], 'contains': ['2304.a1', '3456.i1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 40280426], 'label': '6912.ia.1152.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1152.bf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567423
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.ba1', '576.y1', '576.dl1', '576.ea1', '576.ee1', '576.cl1', '576.cp1', '576.fk1', '576.fu1', '576.fv1', '576.gf1'], 'contains': ['2304.b1', '3456.i1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40315919, 2676], 'label': '6912.ia.1152.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '1152.bg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567424
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mi1', '384.bb1', '384.bc1', '384.bd1', '576.z1', '576.dj1', '576.fs1', '576.gj1'], 'contains': ['2304.c1', '3456.j1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [47537280, 87178291946], 'label': '6912.ia.1152.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '1152.bh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567425
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.bb1', '384.be1', '576.ba1', '576.dr1', '576.ef1', '576.cq1', '576.fl1', '576.fy1', '576.gk1'], 'contains': ['2304.a1', '3456.j1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291946], 'label': '6912.ia.1152.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '1152.bi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567426
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bc1', '384.be1', '576.bb1', '576.dk1', '576.eg1', '576.cr1', '576.fm1', '576.fu1', '576.gg1'], 'contains': ['2304.b1', '3456.j1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [87178327439, 2676], 'label': '6912.ia.1152.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '1152.bj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567427
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bd1', '384.be1', '576.bc1', '576.eh1', '576.cs1', '576.fn1'], 'contains': ['2304.d1', '3456.j1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [87178327439, 93405314676], 'label': '6912.ia.1152.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '1152.bk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567428
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.dt1', '12.du1'], 'contains': ['48.dh1', '48.dr1', '48.ea1', '72.nd1', '72.nk1', '96.bm1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 2676, 87265382400], 'label': '6912.ia.24.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567429
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.bf1', '384.bg1', '384.bh1', '576.bd1', '576.dt1', '576.ei1', '576.ct1', '576.fh1', '576.fj1', '576.ga1', '576.gk1', '576.gl1'], 'contains': ['2304.a1', '3456.k1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 83468087], 'label': '6912.ia.1152.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '1152.bl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567430
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bf1', '384.bi1', '576.be1', '576.dm1', '576.ej1', '576.cu1', '576.fi1', '576.fk1', '576.fw1', '576.gg1', '576.gh1'], 'contains': ['2304.b1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6851, 83468087], 'label': '6912.ia.1152.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '1152.bm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567431
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mo1', '384.bg1', '384.bi1', '576.bf1', '576.dn1', '576.fr1', '576.gj1'], 'contains': ['2304.c1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79833600, 83468087], 'label': '6912.ia.1152.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cu1', 'old_label': '1152.bn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567432
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.mp1', '384.bh1', '384.bi1', '576.bg1', '576.do1'], 'contains': ['2304.f1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [43561327, 83468087], 'label': '6912.ia.1152.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bj1', 'old_label': '1152.bo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567433
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.bj1', '576.bh1', '576.ds1', '576.ef1', '576.ek1', '576.cq1', '576.cv1', '576.fo1', '576.fx1', '576.fz1', '576.gl1'], 'contains': ['2304.a1', '3456.l1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87218571626], 'label': '6912.ia.1152.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1152.bp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567434
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bj1', '576.bi1', '576.dl1', '576.eg1', '576.el1', '576.cr1', '576.cw1', '576.fp1', '576.ft1', '576.fv1', '576.gh1'], 'contains': ['2304.b1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2676, 87218607119], 'label': '6912.ia.1152.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '1152.bq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567435
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bj1', '576.bj1', '576.eh1', '576.em1', '576.cs1', '576.cx1', '576.fq1'], 'contains': ['2304.d1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [93405314676, 87218607119], 'label': '6912.ia.1152.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.jj1', 'old_label': '1152.br1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567436
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.bk1', '384.bl1', '384.bm1', '576.bk1', '576.dt1', '576.en1', '576.cy1', '576.fl1', '576.fo1', '576.ga1', '576.gb1', '576.gi1'], 'contains': ['2304.a1', '3456.m1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [93405312000, 87261759287], 'label': '6912.ia.1152.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '1152.bs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567437
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bk1', '384.bn1', '384.bo1', '576.bl1', '576.dm1', '576.eo1', '576.cz1', '576.fm1', '576.fp1', '576.fw1', '576.ge1', '576.gf1'], 'contains': ['2304.b1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6851, 87261768087], 'label': '6912.ia.1152.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '1152.bt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567438
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ms1', '384.bl1', '384.bn1', '384.bp1', '576.bm1', '576.dn1', '576.fs1', '576.gc1'], 'contains': ['2304.c1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [79833600, 87261759287], 'label': '6912.ia.1152.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hi1', 'old_label': '1152.bu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567439
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '12.dq1', '12.q1', '12.dt1'], 'contains': ['48.e1', '48.dh1', '48.ep1', '72.no1', '72.np1', '96.bn1'], 'core': '48.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36933, 2676, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.24.dq1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567440
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.bk1', '384.bp1', '384.bq1', '576.bn1', '576.ep1', '576.da1', '576.fn1', '576.fq1'], 'contains': ['2304.d1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [93405318851, 87261759287], 'label': '6912.ia.1152.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bc1', 'old_label': '1152.bv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567441
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.mu1', '384.bl1', '384.bo1', '384.bq1', '576.bo1', '576.gd1'], 'contains': ['2304.e1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [93485145600, 87261759287], 'label': '6912.ia.1152.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '1152.bw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567442
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.mv1', '384.bm1', '384.bn1', '384.bq1', '576.bp1', '576.do1'], 'contains': ['2304.f1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [87261768087, 43561327], 'label': '6912.ia.1152.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ci1', 'old_label': '1152.bx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567443
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1152.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.mw1', '384.bm1', '384.bo1', '384.bp1', '384.bq1', '576.bq1'], 'contains': ['2304.g1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': None, 'generators': [93448873327, 87261759287], 'label': '6912.ia.1152.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '576.bq1', 'old_label': '1152.by1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567444
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1', 'complements': ['4.i1'], 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '576.c1', '576.fa1', '576.fb1', '576.fc1', '576.fd1', '576.fe1', '864.a1', '864.fb1', '864.ga1', '864.gb1', '864.gc1', '864.gd1', '864.ge1', '864.gf1'], 'contains': ['3456.d1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40279680], 'label': '6912.ia.1728.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1728.a1', 'normal_contained_in': ['576.b1', '576.c1', '864.a1'], 'normal_contains': ['6912.a1'], 'normalizer': '1.a1', 'old_label': '1728.a1', 'projective_image': '6912.ia', 'quotient_action_image': '6.1', 'quotient_action_kernel': '288.851', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '1728.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 243567445
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '576.g1', '576.h1', '576.i1', '864.c1', '864.y1', '864.z1', '864.ba1', '864.bb1', '864.bc1', '864.bd1', '864.be1'], 'contains': ['3456.a1', '3456.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933], 'label': '6912.ia.1728.c1', 'mobius_quo': None, 'mobius_sub': -288, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1728.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567446
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.d1', '576.e1', '576.f1', '864.a1', '864.c1', '864.d1', '864.e1', '864.f1', '864.g1', '864.h1', '864.i1', '864.j1', '864.k1', '864.l1', '864.m1', '864.n1', '864.p1', '864.q1', '864.o1', '864.s1', '864.r1', '864.t1', '864.u1', '864.v1', '864.w1', '864.x1'], 'contains': ['3456.a1', '3456.d1', '3456.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 40279680], 'label': '6912.ia.1728.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1728.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567447
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.j1', '576.k1', '576.l1', '576.m1', '864.y1', '864.d1', '864.bf1', '864.bg1', '864.bh1', '864.bi1', '864.bj1', '864.bk1', '864.bm1', '864.bl1', '864.bn1'], 'contains': ['3456.a1', '3456.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 36933], 'label': '6912.ia.1728.d1', 'mobius_quo': None, 'mobius_sub': -144, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '1728.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567448
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.n1', '576.o1', '864.c1', '864.e1', '864.bf1', '864.bo1', '864.bp1', '864.bq1', '864.br1', '864.bs1', '864.bt1', '864.bu1', '864.bv1'], 'contains': ['3456.a1', '3456.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 36933], 'label': '6912.ia.1728.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567449
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.p1', '576.q1', '576.r1', '576.s1', '864.z1', '864.f1', '864.bg1', '864.bo1', '864.bw1', '864.bx1', '864.by1', '864.bz1', '864.ca1', '864.cb1', '864.cc1'], 'contains': ['3456.a1', '3456.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36933, 746], 'label': '6912.ia.1728.f1', 'mobius_quo': None, 'mobius_sub': -144, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '1728.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567450
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.a1', '12.m1', '12.o1', '12.x1', '12.y1', '12.cz1', '12.df1', '18.bf1', '18.bp1', '24.bh1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.t1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567451
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '12.q1', '12.du1'], 'contains': ['48.dh1', '48.ei1', '48.ep1', '72.nt1', '72.nu1', '96.bo1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 2676, 83463146], 'label': '6912.ia.24.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567452
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.t1', '576.u1', '576.v1', '576.w1', '864.y1', '864.g1', '864.bf1', '864.bw1', '864.cd1', '864.ce1', '864.cf1', '864.cg1', '864.ci1', '864.ch1', '864.cj1'], 'contains': ['3456.a1', '3456.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 36933], 'label': '6912.ia.1728.g1', 'mobius_quo': None, 'mobius_sub': -48, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1728.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567453
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.x1', '576.y1', '864.ba1', '864.f1', '864.h1', '864.bh1', '864.bp1', '864.bq1', '864.bx1', '864.cd1', '864.ck1', '864.cl1', '864.cm1', '864.cn1', '864.co1', '864.cp1', '864.cq1'], 'contains': ['3456.a1', '3456.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40280426, 36933], 'label': '6912.ia.1728.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '1728.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567454
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.ge1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.z1', '576.ba1', '576.bb1', '576.bc1', '864.z1', '864.i1', '864.bi1', '864.bp1', '864.by1', '864.ce1', '864.ck1', '864.cr1', '864.cs1', '864.ct1', '864.cu1'], 'contains': ['3456.a1', '3456.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 87178291946], 'label': '6912.ia.1728.i1', 'mobius_quo': None, 'mobius_sub': -48, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '1728.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567455
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bd1', '576.be1', '576.bf1', '576.bg1', '864.bb1', '864.j1', '864.bg1', '864.bh1', '864.br1', '864.bz1', '864.ce1', '864.cf1', '864.cl1', '864.cr1', '864.cv1', '864.cw1', '864.cx1', '864.cy1', '864.cz1'], 'contains': ['3456.a1', '3456.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [36933, 83468087], 'label': '6912.ia.1728.j1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '1728.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567456
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bh1', '576.bi1', '576.bj1', '864.ba1', '864.i1', '864.k1', '864.bj1', '864.bo1', '864.bq1', '864.ca1', '864.cf1', '864.cm1', '864.cn1', '864.cs1', '864.cv1', '864.da1', '864.db1', '864.dc1'], 'contains': ['3456.a1', '3456.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87218571626, 36933], 'label': '6912.ia.1728.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1728.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567457
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bk1', '576.bl1', '576.bm1', '576.bn1', '576.bo1', '576.bp1', '576.bq1', '864.bb1', '864.l1', '864.bi1', '864.bj1', '864.br1', '864.bw1', '864.cb1', '864.cd1', '864.co1', '864.ct1', '864.cw1', '864.cx1', '864.da1', '864.dd1', '864.de1'], 'contains': ['3456.a1', '3456.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [36933, 87261759287], 'label': '6912.ia.1728.l1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '1728.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567458
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.br1', '576.bx1', '576.cb1', '864.b1', '864.bc1', '864.m1', '864.bk1', '864.bs1', '864.cc1', '864.cg1', '864.cp1', '864.cu1', '864.cy1', '864.db1', '864.dd1', '864.dg1', '864.df1', '864.dh1', '864.di1', '864.dj1', '864.dk1', '864.dl1', '864.dm1', '864.dn1', '864.do1', '864.dp1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32929, 36933], 'label': '6912.ia.1728.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '864.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '1728.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567459
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bt1', '576.by1', '864.bc1', '864.p1', '864.bm1', '864.bt1', '864.by1', '864.ci1', '864.cm1', '864.cw1', '864.dg1', '864.dq1', '864.dx1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178324129, 36933], 'label': '6912.ia.1728.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '1728.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567460
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bs1', '864.bd1', '864.m1', '864.o1', '864.bl1', '864.bt1', '864.bu1', '864.bx1', '864.ch1', '864.cq1', '864.cs1', '864.cz1', '864.dc1', '864.de1', '864.df1', '864.dq1', '864.dr1', '864.ds1', '864.dt1', '864.du1', '864.dv1', '864.dw1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127403809, 36933], 'label': '6912.ia.1728.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '1728.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567461
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bu1', '576.bz1', '864.be1', '864.r1', '864.bk1', '864.bl1', '864.bv1', '864.bz1', '864.ci1', '864.cj1', '864.cl1', '864.ct1', '864.da1', '864.dh1', '864.dx1', '864.dr1', '864.dy1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 83495329], 'label': '6912.ia.1728.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '1728.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567462
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1', '12.dq1', '12.s1', '12.du1'], 'contains': ['48.f1', '48.dh1', '48.ey1', '72.ny1', '72.nz1', '72.oa1', '96.bp1'], 'core': '48.f1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36933, 87185912426, 2676, 93405312000, 9465, 7620480, 32929], 'label': '6912.ia.24.ds1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ds1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567463
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bv1', '864.bd1', '864.p1', '864.t1', '864.bn1', '864.bs1', '864.bu1', '864.ca1', '864.cj1', '864.ck1', '864.cn1', '864.cx1', '864.di1', '864.dq1', '864.ds1', '864.dy1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218603809, 36933], 'label': '6912.ia.1728.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1728.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567464
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.bw1', '576.ca1', '576.cc1', '864.be1', '864.v1', '864.bm1', '864.bn1', '864.bv1', '864.cb1', '864.cg1', '864.ch1', '864.co1', '864.cr1', '864.cv1', '864.dj1', '864.dx1', '864.dt1', '864.dy1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [36933, 87261786529], 'label': '6912.ia.1728.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '1728.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567465
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.dg1', '576.dp1', '864.c1', '864.eo1', '864.ev1', '864.ew1', '864.ex1', '864.ey1', '864.ez1', '864.fa1', '864.fb1'], 'contains': ['3456.c1', '3456.d1', '3456.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87178328133, 40279680], 'label': '6912.ia.1728.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.s1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567466
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.cd1', '576.ce1', '864.c1', '864.eo1', '864.dz1', '864.ea1', '864.eb1', '864.ec1', '864.ed1'], 'contains': ['3456.c1', '3456.b1', '3456.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40316613, 87178328133], 'label': '6912.ia.1728.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.t1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567467
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['576.dh1', '576.di1', '576.dq1', '864.y1', '864.ev1', '864.dz1', '864.fc1', '864.fd1'], 'contains': ['3456.c1', '3456.e1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7657413, 87178328133], 'label': '6912.ia.1728.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1728.u1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567468
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.ge1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.dj1', '576.dk1', '576.dr1', '864.z1', '864.ew1', '864.ea1', '864.fc1'], 'contains': ['3456.c1', '3456.g1', '3456.j1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178291200, 746], 'label': '6912.ia.1728.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '1728.v1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567469
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.dl1', '576.ds1', '864.ba1', '864.ew1', '864.ex1', '864.ea1', '864.eb1', '864.fd1'], 'contains': ['3456.c1', '3456.i1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40280426, 87178328133], 'label': '6912.ia.1728.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.w1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567470
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.dm1', '576.dn1', '576.do1', '576.dt1', '864.bb1', '864.ey1', '864.ec1', '864.fc1', '864.fd1'], 'contains': ['3456.c1', '3456.k1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87178328133, 83468087], 'label': '6912.ia.1728.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.x1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567471
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.dd1', '576.de1', '576.df1', '864.a1', '864.eo1', '864.ep1', '864.eq1', '864.er1', '864.es1', '864.et1', '864.eu1'], 'contains': ['3456.d1', '3456.b1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40316613, 127370880], 'label': '6912.ia.1728.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1728.y1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567472
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.du1', '576.dv1', '576.dw1', '864.d1', '864.ev1', '864.ep1', '864.fe1', '864.ff1', '864.fg1', '864.fh1', '864.fi1', '864.ga1'], 'contains': ['3456.d1', '3456.e1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7657413, 87091200], 'label': '6912.ia.1728.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1728.z1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567473
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '12.s1', '12.dt1'], 'contains': ['48.dh1', '48.ex1', '48.ey1', '72.oe1', '72.of1', '72.og1', '96.bq1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 2676, 87261754346], 'label': '6912.ia.24.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567474
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.dx1', '576.dy1', '864.e1', '864.eo1', '864.fb1', '864.fe1', '864.fj1', '864.fk1', '864.fl1', '864.fm1', '864.fn1'], 'contains': ['3456.d1', '3456.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87305699013, 40279680], 'label': '6912.ia.1728.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.ba1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567475
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.dz1', '576.ea1', '864.f1', '864.ew1', '864.eq1', '864.ff1', '864.fj1', '864.fo1', '864.fp1', '864.fq1', '864.gb1'], 'contains': ['3456.d1', '3456.g1', '3456.i1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40280426, 40279680], 'label': '6912.ia.1728.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1728.bb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567476
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.eb1', '576.ec1', '864.g1', '864.ev1', '864.er1', '864.fk1', '864.fo1', '864.fr1', '864.fs1', '864.ft1', '864.gc1'], 'contains': ['3456.d1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185948613, 87091200], 'label': '6912.ia.1728.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.bc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567477
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ed1', '576.ee1', '864.h1', '864.ex1', '864.eq1', '864.fg1', '864.fl1', '864.fr1', '864.fu1', '864.fv1', '864.gb1'], 'contains': ['3456.d1', '3456.i1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87096887, 40279680], 'label': '6912.ia.1728.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1728.bd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567478
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ef1', '576.eg1', '576.eh1', '864.i1', '864.ew1', '864.es1', '864.fh1', '864.fl1', '864.fs1', '864.fw1', '864.fx1', '864.gd1'], 'contains': ['3456.d1', '3456.j1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87218571626, 40279680], 'label': '6912.ia.1728.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.be1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567479
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ei1', '576.ej1', '864.j1', '864.ey1', '864.et1', '864.ff1', '864.fm1', '864.fs1', '864.fu1', '864.fy1', '864.ge1'], 'contains': ['3456.d1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87091200, 83468087], 'label': '6912.ia.1728.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1728.bf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567480
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ek1', '576.el1', '576.em1', '864.k1', '864.ex1', '864.es1', '864.fi1', '864.fj1', '864.ft1', '864.fy1', '864.fz1', '864.gd1'], 'contains': ['3456.d1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87265388087, 40279680], 'label': '6912.ia.1728.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.bg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567481
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.en1', '576.eo1', '576.ep1', '864.l1', '864.ey1', '864.eu1', '864.fh1', '864.fn1', '864.fo1', '864.fv1', '864.fz1', '864.gf1'], 'contains': ['3456.d1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87261759287, 87091200], 'label': '6912.ia.1728.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.bh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567482
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.eq1', '576.eu1', '576.ey1', '864.n1', '864.ez1', '864.ep1', '864.fk1', '864.fp1', '864.fu1', '864.fw1', '864.fz1', '864.ga1'], 'contains': ['3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43908480, 87091200], 'label': '6912.ia.1728.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1728.bi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567483
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.er1', '576.ev1', '864.q1', '864.ez1', '864.er1', '864.fe1', '864.fq1', '864.fv1', '864.fx1', '864.fy1', '864.gc1'], 'contains': ['3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87222199680, 87091200], 'label': '6912.ia.1728.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.bj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567484
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.z1', '12.ds1'], 'contains': ['48.dj1', '48.dl1', '48.dn1', '48.du1', '48.dw1', '48.eq1', '48.es1', '72.nm1', '72.oh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 47537280, 7621226, 36933], 'label': '6912.ia.24.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.du1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567485
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.es1', '576.ew1', '864.u1', '864.fa1', '864.et1', '864.fg1', '864.fn1', '864.fp1', '864.ft1', '864.fx1', '864.ge1'], 'contains': ['3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43909226, 87091200], 'label': '6912.ia.1728.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1728.bk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567486
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.et1', '576.ex1', '576.ez1', '864.x1', '864.fa1', '864.eu1', '864.fi1', '864.fm1', '864.fq1', '864.fr1', '864.fw1', '864.gf1'], 'contains': ['3456.d1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87222200426, 87091200], 'label': '6912.ia.1728.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.bl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567487
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cf1', '576.cg1', '576.ch1', '864.d1', '864.dz1', '864.ee1', '864.ef1'], 'contains': ['3456.b1', '3456.e1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 87128133], 'label': '6912.ia.1728.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '1728.bm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567488
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ci1', '576.cj1', '864.e1', '864.eo1', '864.eg1', '864.eh1'], 'contains': ['3456.b1', '3456.f1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40316613, 87305662080], 'label': '6912.ia.1728.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.be1', 'old_label': '1728.bn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567489
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ck1', '576.cl1', '864.f1', '864.ea1', '864.eq1', '864.ee1', '864.eg1', '864.ei1'], 'contains': ['3456.b1', '3456.g1', '3456.i1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 40280426], 'label': '6912.ia.1728.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '1728.bo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567490
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cm1', '576.cn1', '864.g1', '864.dz1', '864.ei1', '864.ej1'], 'contains': ['3456.b1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87185911680, 87128133], 'label': '6912.ia.1728.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1728.bp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567491
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.jb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.co1', '576.cp1', '864.h1', '864.eb1', '864.eq1', '864.eh1', '864.ek1', '864.el1'], 'contains': ['3456.b1', '3456.i1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40316613, 87096887], 'label': '6912.ia.1728.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gr1', 'old_label': '1728.bq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567492
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cq1', '576.cr1', '576.cs1', '864.i1', '864.ea1', '864.es1', '864.ef1', '864.eh1', '864.ej1'], 'contains': ['3456.b1', '3456.j1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40316613, 87218571626], 'label': '6912.ia.1728.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.br1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567493
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ct1', '576.cu1', '864.j1', '864.ec1', '864.ee1', '864.ej1', '864.ek1', '864.em1'], 'contains': ['3456.b1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87128133, 83468087], 'label': '6912.ia.1728.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '1728.bs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567494
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cv1', '576.cw1', '576.cx1', '864.k1', '864.eb1', '864.es1', '864.eg1', '864.em1', '864.en1'], 'contains': ['3456.b1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40316613, 87265388087], 'label': '6912.ia.1728.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ew1', 'old_label': '1728.bt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567495
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.ba1', '8.l1', '12.ds1'], 'contains': ['48.dj1', '48.dm1', '48.do1', '48.dv1', '48.dx1', '48.er1', '48.et1', '72.no1', '72.oi1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [36933, 47537280, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.24.dv1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567496
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.cy1', '576.cz1', '576.da1', '864.l1', '864.ec1', '864.ef1', '864.ei1', '864.el1', '864.en1'], 'contains': ['3456.b1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87128133, 87261759287], 'label': '6912.ia.1728.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1728.bu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567497
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.db1', '864.s1', '864.ed1', '864.ek1', '864.en1'], 'contains': ['3456.b1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 87128133], 'label': '6912.ia.1728.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '1728.bv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567498
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.dc1', '864.w1', '864.ed1', '864.el1', '864.em1'], 'contains': ['3456.b1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [87222232609, 87128133], 'label': '6912.ia.1728.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '1728.bw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567499
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['576.ff1', '576.fg1', '864.bf1', '864.ev1', '864.dz1', '864.gg1', '864.gh1'], 'contains': ['3456.e1', '3456.f1', '3456.h1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7620480, 87265419333], 'label': '6912.ia.1728.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1728.bx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567500
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fh1', '576.fi1', '576.fr1', '864.bg1', '864.fc1', '864.ff1', '864.ee1', '864.gg1'], 'contains': ['3456.e1', '3456.g1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 7621226], 'label': '6912.ia.1728.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '1728.by1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567501
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fj1', '576.fk1', '864.bh1', '864.fd1', '864.ff1', '864.ee1', '864.gh1'], 'contains': ['3456.e1', '3456.i1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [7620480, 83468087], 'label': '6912.ia.1728.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '1728.bz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567502
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fl1', '576.fm1', '576.fn1', '576.fs1', '864.bi1', '864.fc1', '864.fh1', '864.ef1', '864.gh1'], 'contains': ['3456.e1', '3456.j1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7657413, 87185912426], 'label': '6912.ia.1728.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.ca1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567503
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fo1', '576.fp1', '576.fq1', '864.bj1', '864.fd1', '864.fh1', '864.ef1', '864.gg1'], 'contains': ['3456.e1', '3456.l1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7620480, 87261759287], 'label': '6912.ia.1728.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.cb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567504
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.ft1', '576.fx1', '864.bo1', '864.ew1', '864.ea1', '864.fj1', '864.eg1', '864.gg1'], 'contains': ['3456.f1', '3456.g1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87218607813, 746], 'label': '6912.ia.1728.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.cc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567505
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fu1', '576.fy1', '864.bp1', '864.ew1', '864.ea1', '864.fl1', '864.eh1', '864.gh1'], 'contains': ['3456.f1', '3456.i1', '3456.j1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87218570880, 40280426], 'label': '6912.ia.1728.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '1728.cd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567506
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '8.l1', '12.dp1'], 'contains': ['48.dp1', '48.dy1', '48.ew1', '72.np1', '72.oi1', '96.bs1'], 'core': '144.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 9465, 7620480, 32929, 7621226], 'label': '6912.ia.24.dw1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '24.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567507
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ho1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fv1', '576.fz1', '864.bq1', '864.ex1', '864.eb1', '864.fj1', '864.fl1', '864.eg1', '864.eh1'], 'contains': ['3456.f1', '3456.i1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87218607813, 87096887], 'label': '6912.ia.1728.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ho1', 'old_label': '1728.ce1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ce1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567508
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.fw1', '576.ga1', '864.br1', '864.ey1', '864.ec1', '864.gg1', '864.gh1'], 'contains': ['3456.f1', '3456.k1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [83468087, 87265382400], 'label': '6912.ia.1728.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.cf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567509
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.gb1', '576.gc1', '576.gd1', '576.ge1', '864.bw1', '864.fc1', '864.fo1', '864.ei1', '864.gg1'], 'contains': ['3456.g1', '3456.h1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87185948613, 87185912426], 'label': '6912.ia.1728.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.cg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567510
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.gf1', '576.gi1', '864.cd1', '864.fd1', '864.fo1', '864.ei1', '864.gh1'], 'contains': ['3456.h1', '3456.i1', '3456.m1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87185948613, 87261759287], 'label': '6912.ia.1728.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.ch1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567511
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.gg1', '576.gj1', '576.gk1', '864.ce1', '864.fc1', '864.fs1', '864.ej1', '864.gh1'], 'contains': ['3456.h1', '3456.j1', '3456.k1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87185948613, 7621226], 'label': '6912.ia.1728.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.ci1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567512
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '1728.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.gh1', '576.gl1', '864.cf1', '864.fd1', '864.fs1', '864.ej1', '864.gg1'], 'contains': ['3456.h1', '3456.k1', '3456.l1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [87185948613, 83468087], 'label': '6912.ia.1728.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '1728.cj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567513
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['768.a1', '768.b1', '768.c1', '1152.a1', '1152.b1', '1152.o1', '1152.i1', '1152.r1', '1152.w1', '1152.x1', '1152.bc1', '1152.bf1', '1152.bi1', '1152.bl1', '1152.bp1', '1152.bs1'], 'contains': ['6912.a1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93405312000], 'label': '6912.ia.2304.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '2304.a1', 'normal_contained_in': ['576.b1', '1152.a1', '1152.b1'], 'normal_contains': ['6912.a1'], 'normalizer': '1.a1', 'old_label': '2304.a1', 'projective_image': '6912.ia', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1152.157461', 'quotient_action_kernel_order': 1152, 'quotient_fusion': None, 'short_label': '2304.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567514
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.a1', '768.d1', '768.e1', '1152.c1', '1152.l1', '1152.p1', '1152.j1', '1152.s1', '1152.v1', '1152.ba1', '1152.bb1', '1152.bg1', '1152.bj1', '1152.bm1', '1152.bq1', '1152.bt1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2676], 'label': '6912.ia.2304.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '2304.b1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567515
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.c1', '768.b1', '768.d1', '768.f1', '1152.d1', '1152.m1', '1152.u1', '1152.y1', '1152.bd1', '1152.bh1', '1152.bn1', '1152.bu1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [47537280], 'label': '6912.ia.2304.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '576.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '2304.c1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567516
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.a1', '768.f1', '768.g1', '1152.e1', '1152.q1', '1152.k1', '1152.t1', '1152.bk1', '1152.br1', '1152.bv1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93405314676], 'label': '6912.ia.2304.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '2304.d1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567517
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bb1', '12.ds1'], 'contains': ['48.dk1', '48.dl1', '48.dm1', '48.ej1', '48.el1', '48.ez1', '48.fb1', '72.nw1', '72.oj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178324129, 7654690, 47537280, 36933], 'label': '6912.ia.24.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dx1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567518
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.fc1', '768.b1', '768.e1', '768.g1', '1152.f1', '1152.z1', '1152.be1', '1152.bw1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [93452849280], 'label': '6912.ia.2304.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '2304.e1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567519
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.fd1', '768.c1', '768.d1', '768.g1', '1152.g1', '1152.n1', '1152.bo1', '1152.bx1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120116474], 'label': '6912.ia.2304.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '2304.f1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567520
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2304.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.fe1', '768.c1', '768.e1', '768.f1', '768.g1', '1152.h1', '1152.by1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [93525428474], 'label': '6912.ia.2304.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.g1', 'old_label': '2304.g1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2304.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 243567521
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1152.a1', '1152.c1', '1152.d1', '1152.e1', '1152.f1', '1152.g1', '1152.h1', '1728.c1', '1728.b1', '1728.d1', '1728.e1', '1728.f1', '1728.g1', '1728.h1', '1728.i1', '1728.j1', '1728.k1', '1728.l1', '1728.m1', '1728.o1', '1728.n1', '1728.p1', '1728.q1', '1728.r1'], 'contains': ['6912.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36933], 'label': '6912.ia.3456.a1', 'mobius_quo': -1, 'mobius_sub': 3456, 'normal_closure': '3456.a1', 'normal_contained_in': ['864.a1', '864.b1', '1152.a1'], 'normal_contains': ['6912.a1'], 'normalizer': '1.a1', 'old_label': '3456.a1', 'projective_image': '3456.jo', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3456.jo', 'quotient_action_kernel_order': 3456, 'quotient_fusion': None, 'short_label': '3456.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567522
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1152.b1', '1152.l1', '1152.m1', '1152.n1', '1728.c1', '1728.bf1', '1728.s1', '1728.bg1', '1728.bh1', '1728.bi1', '1728.bj1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87178291200], 'label': '6912.ia.3456.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1152.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3456.b1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567523
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.o1', '1152.p1', '1152.q1', '1728.a1', '1728.b1', '1728.bf1', '1728.be1', '1728.bk1', '1728.bl1', '1728.bm1', '1728.bn1', '1728.bo1', '1728.bp1', '1728.bq1', '1728.br1', '1728.bs1', '1728.bt1', '1728.bu1', '1728.bv1', '1728.bw1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40279680], 'label': '6912.ia.3456.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3456.c1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567524
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.i1', '1152.j1', '1152.k1', '1728.b1', '1728.s1', '1728.be1', '1728.t1', '1728.u1', '1728.v1', '1728.w1', '1728.x1', '1728.y1', '1728.z1', '1728.ba1', '1728.bb1', '1728.bc1', '1728.bd1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40316613], 'label': '6912.ia.3456.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3456.d1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567525
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1152.r1', '1152.s1', '1152.t1', '1152.u1', '1728.d1', '1728.bg1', '1728.bk1', '1728.t1', '1728.bx1', '1728.by1', '1728.bz1', '1728.ca1', '1728.cb1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7657413], 'label': '6912.ia.3456.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '3456.e1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567526
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1152.v1', '1152.w1', '1728.e1', '1728.bf1', '1728.s1', '1728.bl1', '1728.u1', '1728.bx1', '1728.cc1', '1728.cd1', '1728.ce1', '1728.cf1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87218570880], 'label': '6912.ia.3456.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '3456.f1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567527
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.x1', '1152.y1', '1152.z1', '1152.ba1', '1728.f1', '1728.bh1', '1728.bm1', '1728.v1', '1728.by1', '1728.cc1', '1728.cg1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [746], 'label': '6912.ia.3456.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '3456.g1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567528
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bc1', '8.m1', '12.ds1'], 'contains': ['48.dk1', '48.dn1', '48.do1', '48.ek1', '48.em1', '48.fa1', '48.fc1', '72.ny1', '72.ok1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.24.dy1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dy1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567529
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1152.bb1', '1152.bc1', '1152.bd1', '1152.be1', '1728.g1', '1728.bg1', '1728.bn1', '1728.w1', '1728.bx1', '1728.cg1', '1728.ch1', '1728.ci1', '1728.cj1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87185948613], 'label': '6912.ia.3456.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '3456.h1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567530
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.gp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.bf1', '1152.bg1', '1728.h1', '1728.bi1', '1728.bm1', '1728.bo1', '1728.v1', '1728.x1', '1728.bz1', '1728.cd1', '1728.ce1', '1728.ch1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40280426], 'label': '6912.ia.3456.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gp1', 'old_label': '3456.i1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567531
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.ge1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.bh1', '1152.bi1', '1152.bj1', '1152.bk1', '1728.i1', '1728.bh1', '1728.bp1', '1728.y1', '1728.ca1', '1728.cd1', '1728.ci1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [87178291946], 'label': '6912.ia.3456.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ge1', 'old_label': '3456.j1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567532
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.bl1', '1152.bm1', '1152.bn1', '1152.bo1', '1728.j1', '1728.bj1', '1728.bq1', '1728.z1', '1728.by1', '1728.bz1', '1728.cf1', '1728.ci1', '1728.cj1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [83468087], 'label': '6912.ia.3456.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '3456.k1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567533
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.eu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.bp1', '1152.bq1', '1152.br1', '1728.k1', '1728.bi1', '1728.bp1', '1728.br1', '1728.y1', '1728.ba1', '1728.cb1', '1728.cc1', '1728.ce1', '1728.cj1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [87218571626], 'label': '6912.ia.3456.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.eu1', 'old_label': '3456.l1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567534
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3456.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1152.bs1', '1152.bt1', '1152.bu1', '1152.bv1', '1152.bw1', '1152.bx1', '1152.by1', '1728.l1', '1728.bj1', '1728.bs1', '1728.bb1', '1728.ca1', '1728.cb1', '1728.cf1', '1728.cg1', '1728.ch1'], 'contains': ['6912.a1'], 'core': '6912.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [87261759287], 'label': '6912.ia.3456.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1', 'old_label': '3456.m1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567535
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6912.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2304.a1', '2304.b1', '2304.c1', '2304.d1', '2304.e1', '2304.f1', '2304.g1', '3456.a1', '3456.c1', '3456.d1', '3456.b1', '3456.e1', '3456.f1', '3456.g1', '3456.h1', '3456.i1', '3456.j1', '3456.k1', '3456.l1', '3456.m1'], 'contains': [], 'core': '6912.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '6912.ia.6912.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '6912.a1', 'normal_contained_in': ['1728.a1', '2304.a1', '3456.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6912.a1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6912.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 243567536
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1', '8.m1', '12.dp1'], 'contains': ['48.dp1', '48.en1', '48.ff1', '72.nz1', '72.ok1', '96.bu1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 120115956, 9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.24.dz1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567537
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.be1', '8.m1'], 'contains': ['48.dq1', '48.eo1', '48.fh1', '72.oa1', '72.ok1', '96.bv1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93525427956, 9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.24.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ea1', 'old_label': '24.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ea1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567538
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.bs1', '12.bt1', '12.bu1', '12.db1', '12.dc1', '12.dh1', '12.di1', '18.bg1', '18.bo1', '24.dl1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 87178291200, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.6.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567539
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.u1', '12.dt1'], 'contains': ['48.e1', '48.dr1', '48.ex1', '72.ol1', '72.os1', '96.by1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933, 746, 2676], 'label': '6912.ia.24.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567540
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.w1', '12.du1'], 'contains': ['48.f1', '48.dr1', '48.ei1', '72.om1', '72.ow1', '96.bz1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 40280426, 36933, 2676], 'label': '6912.ia.24.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567541
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.u1', '12.w1'], 'contains': ['48.dr1', '48.ei1', '48.ex1', '72.on1', '72.pa1', '96.ca1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933, 2676, 127371626], 'label': '6912.ia.24.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ed1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567542
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.dt1', '12.du1'], 'contains': ['48.dr1', '48.ep1', '48.ey1', '72.oo1', '72.pf1', '96.cb1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 7621226, 36933, 2676, 87265382400], 'label': '6912.ia.24.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ee1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567543
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bf1', '12.ds1'], 'contains': ['48.dt1', '48.du1', '48.dv1', '48.ee1', '48.eg1', '48.ez1', '48.fa1', '72.pi1', '72.pl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.24.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ef1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567544
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bg1', '8.n1', '12.ds1'], 'contains': ['48.dt1', '48.dw1', '48.dx1', '48.ef1', '48.eh1', '48.fb1', '48.fc1', '72.pk1', '72.pm1', '72.pn1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.24.eg1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eg1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567545
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1', '12.dq1', '12.z1', '12.dt1'], 'contains': ['48.e1', '48.ea1', '48.ey1', '72.pk1', '72.po1', '96.ch1'], 'core': '48.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 2676, 93405312000, 9465, 32929], 'label': '6912.ia.24.eh1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567546
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bi1', '8.n1', '12.dp1'], 'contains': ['48.dy1', '48.eb1', '48.ff1', '72.pm1', '72.po1', '96.ci1'], 'core': '144.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 87185911680, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.24.ei1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ei1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567547
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bj1', '8.n1'], 'contains': ['48.dz1', '48.ec1', '48.fg1', '72.pn1', '72.po1', '96.cj1'], 'core': '144.d1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 87185911680, 36933, 87185912426, 93525427956, 9465, 32929], 'label': '6912.ia.24.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '24.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ej1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567548
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '12.z1', '12.du1'], 'contains': ['48.ea1', '48.ei1', '48.ey1', '72.pp1', '72.pv1', '96.ck1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 2676, 87261754346], 'label': '6912.ia.24.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ek1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567549
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.c1'], 'contains': ['12.b1', '12.bs1', '12.bv1', '12.da1', '12.dd1', '12.dg1', '12.dj1', '18.bh1', '18.bp1', '24.dm1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.v1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567550
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bk1', '8.o1', '12.dp1'], 'contains': ['48.eb1', '48.en1', '48.ew1', '72.pq1', '72.px1', '96.cl1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 47537280, 9465, 32929, 7621226], 'label': '6912.ia.24.el1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '24.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.el1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567551
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1', '12.dq1', '12.bd1', '12.du1'], 'contains': ['48.f1', '48.ea1', '48.ep1', '72.pq1', '72.qb1', '96.cm1'], 'core': '48.f1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87185911680, 36933, 2676, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.24.em1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.em1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567552
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '12.bd1', '12.dt1'], 'contains': ['48.ea1', '48.ep1', '48.ex1', '72.pr1', '72.qf1', '96.cn1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 2676, 83463146], 'label': '6912.ia.24.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.en1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567553
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bm1', '12.ds1'], 'contains': ['48.ed1', '48.ee1', '48.ef1', '48.ej1', '48.ek1', '48.eq1', '48.er1', '72.pw1', '72.pz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.24.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eo1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567554
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bn1', '8.o1', '12.ds1'], 'contains': ['48.ed1', '48.eg1', '48.eh1', '48.el1', '48.em1', '48.es1', '48.et1', '72.px1', '72.qb1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 36933, 47537280, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.24.ep1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '24.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ep1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567555
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '12.bl1'], 'contains': ['48.fr1', '48.fs1', '48.ft1', '48.gl1', '48.gn1', '48.gr1', '48.gt1', '72.qi1', '72.qj1', '96.ee1'], 'core': '288.f1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 43909226, 47537280, 87178328133, 40279680], 'label': '6912.ia.24.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '24.eq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.er1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567556
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.bn1'], 'contains': ['48.fk1', '48.fl1', '48.fm1', '48.fu1', '48.fv1', '48.fw1', '48.fx1', '48.fn1', '48.fo1', '48.fp1', '48.fq1', '48.ge1', '48.gf1', '48.gg1', '48.gh1', '72.qg1', '72.qh1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 40316613, 43909226, 93405312000, 87178291200, 2676, 127407813], 'label': '6912.ia.24.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.er1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567557
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '12.bn1'], 'contains': ['48.fu1', '48.fv1', '48.fw1', '48.fx1', '48.fy1', '48.ga1', '48.gb1', '48.ge1', '48.gf1', '48.gg1', '48.gh1', '48.gi1', '48.gj1', '48.gq1', '48.gu1', '72.qi1', '72.qk1'], 'core': '288.e1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 87178328133, 2676, 40279680], 'label': '6912.ia.24.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '24.es1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.es1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567558
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '24.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.p1', '12.bo1'], 'contains': ['48.g1', '48.fz1', '48.gc1', '48.gk1', '48.gm1', '48.gp1', '48.gv1', '72.qj1', '72.qk1', '96.ep1'], 'core': '48.g1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 47537280, 43944719, 87178328133, 40279680], 'label': '6912.ia.24.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '24.et1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.et1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567559
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1', '9.c1'], 'contains': ['54.a1', '54.b1', '54.c1', '54.d1', '54.e1', '54.f1', '54.g1', '54.h1', '54.q1', '54.r1', '54.s1', '54.t1', '54.u1', '54.v1', '54.w1', '54.i1', '54.j1', '54.k1', '54.l1', '54.m1', '54.n1', '54.o1', '54.p1', '54.x1', '54.y1', '54.z1', '54.ba1', '54.bb1', '54.bc1', '54.bd1', '54.be1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.27.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243567560
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['12.bw1', '12.de1', '12.dk1', '18.bi1', '18.bp1', '24.bj1', '24.dn1', '24.do1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 43909226, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.6.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '6.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
  • id: 243567561
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.i1', '16.h1'], 'contains': ['64.a1', '64.b1', '64.d1', '64.h1', '96.z1', '96.bc1', '96.bd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 87178291200, 47537280, 36933], 'label': '6912.ia.32.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567562
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.j1', '16.h1'], 'contains': ['64.a1', '64.c1', '64.e1', '64.i1', '96.ba1', '96.be1', '96.bf1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.32.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567563
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.k1', '16.h1'], 'contains': ['64.a1', '64.f1', '64.g1', '64.j1', '96.bb1', '96.bh1', '96.bi1', '96.bj1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [43576538, 93405312000, 87178291200, 79833600, 36933, 83468087], 'label': '6912.ia.32.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567564
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1'], 'contains': ['64.k1', '96.a1', '96.t1', '96.u1', '96.v1', '96.w1', '96.x1', '96.y1', '128.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.32.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567565
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '8.l1', '16.h1'], 'contains': ['64.b1', '64.c1', '64.f1', '64.l1', '96.bn1', '96.br1', '96.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.32.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567566
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '8.m1', '16.h1'], 'contains': ['64.b1', '64.e1', '64.g1', '64.m1', '96.bp1', '96.bt1', '96.bu1', '96.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.32.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567567
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '8.n1', '16.h1'], 'contains': ['64.c1', '64.d1', '64.g1', '64.n1', '96.cc1', '96.ch1', '96.ci1', '96.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 87185911680, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.32.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567568
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '8.o1', '16.h1'], 'contains': ['64.d1', '64.e1', '64.f1', '64.o1', '96.cl1', '96.cm1', '96.co1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 87185911680, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.32.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567569
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.i1', '16.j1', '16.k1', '16.l1', '16.m1', '16.n1', '16.o1'], 'contains': ['96.b1', '96.de1', '96.dg1', '96.di1', '96.dj1', '96.dk1', '96.dl1', '128.a1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.32.i1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '32.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567570
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.p1', '16.q1', '16.r1'], 'contains': ['64.k1', '96.c1', '96.ed1', '96.el1', '96.em1', '128.b1'], 'core': '96.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 87178328133, 40279680], 'label': '6912.ia.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.j1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567571
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.h1', '3456.e1', '3456.j1', '3456.l1', '3456.g1', '3456.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.f1', '4.g1', '6.n1', '6.t1', '6.v1', '6.w1', '8.d1', '8.k1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 43909226, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.f1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243567572
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.p1', '12.q1', '12.t1', '12.u1', '12.x1', '12.bb1', '12.bj1', '18.m1', '18.p1', '24.k1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 2676, 87218570880, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.6.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567573
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '16.h1'], 'contains': ['64.h1', '64.i1', '64.j1', '64.l1', '64.m1', '64.n1', '64.o1', '96.ee1', '96.en1', '96.ep1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [120115956, 93405312000, 7657413, 47537280, 7621226, 87178328133], 'label': '6912.ia.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '32.k1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567574
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.p1', '16.s1', '16.t1'], 'contains': ['64.k1', '96.d1', '96.fm1', '96.fn1', '96.fo1', '128.c1'], 'core': '96.d1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 7657413, 47537280, 40279680], 'label': '6912.ia.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.l1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567575
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '16.q1', '16.s1', '16.u1'], 'contains': ['64.k1', '96.fp1', '96.fq1', '96.fr1', '96.fs1', '128.d1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 40315919, 40279680], 'label': '6912.ia.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.m1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567576
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.p1', '16.u1', '16.v1'], 'contains': ['64.k1', '96.e1', '96.ft1', '96.fu1', '96.fv1', '128.e1'], 'core': '96.e1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 87185948613, 40279680], 'label': '6912.ia.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.n1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567577
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.q1', '16.t1', '16.v1'], 'contains': ['64.k1', '96.fw1', '96.fx1', '96.fy1', '96.fz1', '128.f1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 87218607119, 40279680], 'label': '6912.ia.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.o1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567578
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '16.r1', '16.s1', '16.v1'], 'contains': ['64.k1', '96.ga1', '96.gb1', '96.gc1', '96.gd1', '128.g1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 43944719, 40279680], 'label': '6912.ia.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.p1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567579
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '16.r1', '16.t1', '16.u1'], 'contains': ['64.k1', '96.ge1', '96.gf1', '96.gg1', '96.gh1', '96.gi1', '96.gj1', '96.gk1', '128.h1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 87222200426, 47537280, 40279680], 'label': '6912.ia.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.q1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567580
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': ['192.dx1', '192.dk1', '192.dm1', '192.dn1', '192.du1', '192.dv1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.b1', '12.bw1', '18.bl1', '18.bn1', '18.bp1'], 'contains': ['72.a1', '72.bf1', '72.bg1', '72.jd1', '72.dh1', '72.di1', '72.kz1', '108.fc1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.36.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1'], 'normal_contains': ['72.a1', '144.a1', '144.c1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '3456.jo', 'quotient_action_image': '36.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567581
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['192.ci1', '192.dr1', '192.ck1', '192.dz1', '192.dy1', '192.dw1', '192.dt1', '192.dv1', '192.cg1', '192.dp1', '192.ch1', '192.do1', '192.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.d1', '12.ce1', '18.bb1', '18.by1', '18.ca1'], 'contains': ['72.c1', '72.jo1', '72.li1', '108.fj1', '144.jv1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.b1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.b1', 'normal_contained_in': ['12.c1', '12.d1'], 'normal_contains': ['72.c1', '144.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567582
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': ['192.cj1', '192.ck1', '192.ce1', '192.dl1', '192.dn1', '192.ea1'], 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.f1', '12.cl1', '18.be1', '18.bs1', '18.cg1'], 'contains': ['72.b1', '72.ee1', '72.fj1', '108.fp1', '144.gc1'], 'core': '36.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.c1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.c1', 'normal_contained_in': ['12.e1', '12.f1'], 'normal_contains': ['72.b1', '144.d1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '3456.jo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567583
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.p1', '12.r1', '12.s1', '12.w1', '12.y1', '12.bg1', '12.bi1', '18.n1', '18.r1', '24.l1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 2676, 87218570880, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.6.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567584
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.a1', '18.b1', '18.y1'], 'contains': ['72.h1', '72.lw1', '72.ci1', '72.ef1', '72.nd1', '108.g1', '144.e1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567585
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.a1', '18.c1', '18.be1'], 'contains': ['72.h1', '72.mc1', '72.md1', '72.ee1', '72.fw1', '72.ol1', '72.om1', '108.m1', '144.f1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40280426, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567586
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.b1', '18.d1', '18.be1'], 'contains': ['72.h1', '72.md1', '72.fj1', '72.gr1', '72.on1', '108.r1', '144.g1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567587
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '18.a1', '18.d1', '18.bf1'], 'contains': ['72.h1', '72.me1', '72.gh1', '72.hb1', '72.oo1', '108.v1', '144.h1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87178291200, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567588
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '18.c1', '18.d1', '18.y1'], 'contains': ['72.h1', '72.il1', '72.im1', '108.bc1', '144.i1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43908480, 87178291200, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567589
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.b1', '18.c1', '18.bf1'], 'contains': ['72.h1', '72.in1', '72.io1', '108.bd1', '144.j1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43909226, 32929, 87178291200, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567590
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '12.bl1', '12.bn1'], 'contains': ['72.d1', '72.e1', '72.f1', '72.g1', '72.ir1', '72.iu1', '72.iv1', '72.bj1', '72.bk1', '72.ck1', '72.cl1', '72.jg1', '72.ji1', '72.kd1', '72.ke1', '72.qg1', '72.qi1', '108.eu1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.36.gd1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '36.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567591
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '12.bo1', '18.z1'], 'contains': ['72.is1', '72.it1', '72.iw1', '72.jm1', '72.jn1', '72.jr1', '72.kf1', '72.qj1', '108.eu1', '144.hi1'], 'core': '144.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.ge1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '36.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ge1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567592
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.z1', '18.ba1', '18.bb1'], 'contains': ['72.is1', '72.iy1', '72.iz1', '72.jo1', '72.jp1', '72.kj1', '72.kk1', '108.ev1', '144.hj1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gf1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567593
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '18.z1'], 'contains': ['72.it1', '72.iw1', '72.iz1', '72.jw1', '72.jy1', '72.km1', '72.kn1', '108.ew1', '144.hk1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '36.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567594
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.u1', '12.v1', '12.y1', '12.z1', '12.ba1', '12.be1', '12.bk1', '18.s1', '18.v1', '24.n1'], 'core': '48.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 43908480, 2676, 87218570880, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.6.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567595
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '18.z1', '18.bc1', '18.bd1'], 'contains': ['72.it1', '72.iy1', '72.jt1', '72.kb1', '72.ko1', '108.ex1', '144.hl1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gh1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567596
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '18.z1', '18.bg1', '18.bh1'], 'contains': ['72.iw1', '72.iy1', '72.ku1', '72.kv1', '72.kx1', '108.ey1', '144.hm1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gi1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567597
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.bm1', '18.y1', '18.be1', '18.bf1'], 'contains': ['72.b1', '72.h1', '72.cm1', '108.fc1', '144.ft1'], 'core': '72.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.gj1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567598
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '18.bb1', '18.bc1', '18.bg1'], 'contains': ['72.iy1', '72.iz1', '72.li1', '72.lj1', '72.lo1', '108.ez1', '144.ho1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.36.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gk1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567599
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '18.ba1', '18.bd1', '18.bg1'], 'contains': ['72.iy1', '72.lk1', '72.ll1', '108.fa1', '144.hp1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.36.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567600
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.ba1', '18.bc1', '18.bh1'], 'contains': ['72.iy1', '72.lm1', '72.ln1', '108.fb1', '144.hq1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87178291200, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.36.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567601
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.bm1', '18.bb1', '18.bd1', '18.bh1'], 'contains': ['72.c1', '72.iy1', '72.lh1', '108.fc1', '144.hr1'], 'core': '72.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.gn1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gn1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567602
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '12.bw1', '18.bi1'], 'contains': ['72.lu1', '108.fc1', '144.fv1', '144.hs1', '144.ht1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.36.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '36.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.go1', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 243567603
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dp1', '12.dq1', '18.a1'], 'contains': ['72.lw1', '72.mc1', '72.me1', '72.np1', '72.nz1', '72.po1', '72.pq1', '108.gi1', '144.hg1'], 'core': '144.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 7621226, 36933, 2676], 'label': '6912.ia.36.jw1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567604
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '18.a1'], 'contains': ['72.lw1', '72.md1', '72.me1', '72.nu1', '72.of1', '72.pp1', '72.pr1', '108.gk1', '144.hh1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 36933, 2676, 83463146], 'label': '6912.ia.36.jx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567605
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.v1', '12.w1', '12.x1', '12.bc1', '12.bd1', '12.bf1', '12.bh1', '18.t1', '18.x1', '24.o1'], 'core': '48.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43908480, 2676, 87218570880, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.6.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567606
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '12.dp1', '12.ds1'], 'contains': ['72.lx1', '72.ly1', '72.lz1', '72.ma1', '72.mb1', '72.mf1', '72.mg1', '72.oh1', '72.oi1', '72.oj1', '72.ok1', '72.pl1', '72.pm1', '72.pw1', '72.px1', '108.gi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.36.jy1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '36.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jy1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567607
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1'], 'contains': ['72.i1', '72.j1', '72.l1', '72.o1', '72.p1', '72.s1', '72.v1', '72.bq1', '72.br1', '72.bt1', '72.bw1', '72.dl1', '72.dm1', '72.eg1', '72.ej1', '108.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127380345, 43909226, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567608
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.f1', '18.bj1'], 'contains': ['72.i1', '72.k1', '72.m1', '72.q1', '72.w1', '72.mj1', '72.mk1', '72.ml1', '72.bp1', '72.bs1', '72.bx1', '72.dk1', '72.dt1', '72.ek1', '72.ne1', '72.nf1', '72.ng1', '108.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567609
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.h1', '18.bj1'], 'contains': ['72.j1', '72.k1', '72.t1', '72.u1', '72.ba1', '72.bu1', '72.bv1', '72.by1', '72.eh1', '72.ei1', '72.el1', '108.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567610
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.g1', '18.bk1'], 'contains': ['72.k1', '72.bb1', '72.bd1', '72.mn1', '72.mo1', '72.cb1', '72.cd1', '72.eo1', '72.eq1', '72.ni1', '72.nj1', '108.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567611
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.h1', '18.bk1'], 'contains': ['72.k1', '72.bc1', '72.be1', '72.cc1', '72.ce1', '72.ep1', '72.er1', '108.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567612
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.g1', '18.bl1'], 'contains': ['72.k1', '72.l1', '72.z1', '72.bf1', '72.bi1', '72.ca1', '72.cf1', '72.ch1', '72.en1', '72.es1', '72.eu1', '108.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 87178291200, 40297548, 36933], 'label': '6912.ia.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567613
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.f1', '18.h1', '18.bl1'], 'contains': ['72.k1', '72.y1', '72.bg1', '72.mm1', '72.mp1', '72.bz1', '72.cg1', '72.em1', '72.et1', '72.nh1', '72.nk1', '108.g1'], 'core': '144.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87178291200, 36933, 87124129, 87109068], 'label': '6912.ia.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567614
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1'], 'contains': ['72.m1', '72.n1', '72.p1', '72.r1', '72.t1', '72.v1', '72.bh1', '72.dp1', '72.dq1', '72.dr1', '72.ds1', '72.ev1', '72.ew1', '72.fk1', '72.fl1', '108.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 93405312000, 87178291200, 36933, 119750400, 87091200], 'label': '6912.ia.36.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567941
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1', '16.b1', '24.bs1'], 'contains': ['96.x1', '96.fo1', '144.b1', '144.fy1', '192.j1'], 'core': '144.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [7620480, 93525427956, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.48.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '48.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567615
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.j1', '18.bj1'], 'contains': ['72.n1', '72.o1', '72.q1', '72.x1', '72.ba1', '72.dn1', '72.do1', '72.du1', '72.dw1', '72.fm1', '72.fo1', '108.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 87178291200, 43945413, 36933, 87100665], 'label': '6912.ia.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567616
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.b1'], 'contains': ['12.e1', '12.q1', '12.r1', '12.ba1', '12.bf1', '12.bx1', '12.cz1', '18.br1', '18.bs1', '24.bm1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.x1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.x1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243567617
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.j1', '18.bm1'], 'contains': ['72.q1', '72.z1', '72.be1', '72.dy1', '72.eb1', '72.fq1', '72.ft1', '108.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567618
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.i1', '18.bm1'], 'contains': ['72.q1', '72.y1', '72.bd1', '72.mr1', '72.mv1', '72.dx1', '72.ea1', '72.fp1', '72.fs1', '72.or1', '72.ov1', '108.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567619
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.i1', '18.bn1'], 'contains': ['72.q1', '72.bc1', '72.bf1', '72.mq1', '72.mu1', '72.dz1', '72.ec1', '72.fr1', '72.fu1', '72.oq1', '72.ou1', '108.l1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 87178291200, 40297548, 36933, 746], 'label': '6912.ia.36.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567620
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.f1', '18.j1', '18.bn1'], 'contains': ['72.q1', '72.bb1', '72.bg1', '72.mq1', '72.ms1', '72.mt1', '72.mw1', '72.dv1', '72.ed1', '72.fn1', '72.fv1', '72.op1', '72.os1', '72.ot1', '72.ow1', '108.m1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.36.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567621
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.l1', '18.bj1'], 'contains': ['72.r1', '72.s1', '72.u1', '72.w1', '72.x1', '72.ex1', '72.ey1', '72.ez1', '72.fa1', '72.fy1', '72.gi1', '108.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 87178291200, 43945413, 36933, 87100665], 'label': '6912.ia.36.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567622
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.l1', '18.bm1'], 'contains': ['72.u1', '72.z1', '72.bd1', '72.fd1', '72.fg1', '72.gl1', '72.go1', '108.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.36.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567623
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.k1', '18.bm1'], 'contains': ['72.u1', '72.y1', '72.be1', '72.mx1', '72.fc1', '72.ff1', '72.gk1', '72.gn1', '72.pb1', '108.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.36.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567624
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.k1', '18.bn1'], 'contains': ['72.u1', '72.bb1', '72.bf1', '72.mt1', '72.mu1', '72.fe1', '72.fh1', '72.gm1', '72.gp1', '72.oy1', '72.oz1', '108.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40280426, 87178291200, 40297548, 36933], 'label': '6912.ia.36.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567625
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.h1', '18.l1', '18.bn1'], 'contains': ['72.u1', '72.bc1', '72.bg1', '72.mu1', '72.mw1', '72.fb1', '72.fi1', '72.gj1', '72.gq1', '72.ox1', '72.pa1', '108.r1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.36.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567626
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.l1', '18.bo1'], 'contains': ['72.w1', '72.z1', '72.bc1', '72.gb1', '72.ge1', '72.gv1', '72.gy1', '108.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.36.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567627
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.b1'], 'contains': ['12.h1', '12.s1', '12.t1', '12.bh1', '12.bk1', '12.bx1', '12.df1', '18.bu1', '18.bv1', '18.bw1', '24.bn1'], 'core': '12.h1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.y1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.y1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567628
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.k1', '18.bo1'], 'contains': ['72.w1', '72.y1', '72.bb1', '72.mz1', '72.na1', '72.ga1', '72.gd1', '72.gu1', '72.gx1', '72.pd1', '72.pe1', '108.s1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 87178291200, 36933, 87100665, 83480268], 'label': '6912.ia.36.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567629
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.k1', '18.bp1'], 'contains': ['72.w1', '72.be1', '72.bf1', '72.nc1', '72.gc1', '72.gf1', '72.gw1', '72.gz1', '72.pg1', '108.u1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.36.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567630
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '18.f1', '18.l1', '18.bp1'], 'contains': ['72.w1', '72.bd1', '72.bg1', '72.my1', '72.nb1', '72.fz1', '72.gg1', '72.gt1', '72.ha1', '72.pc1', '72.pf1', '108.v1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.36.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567631
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.k1', '18.bk1'], 'contains': ['72.x1', '72.bb1', '72.be1', '72.hf1', '72.hh1', '72.ho1', '72.hq1', '108.w1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.36.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567632
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.l1', '18.bk1'], 'contains': ['72.x1', '72.bc1', '72.bd1', '72.hg1', '72.hi1', '72.hp1', '72.hr1', '108.x1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.36.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567633
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.k1', '18.bl1'], 'contains': ['72.x1', '72.y1', '72.bf1', '72.bh1', '72.bi1', '72.he1', '72.hj1', '72.hn1', '72.ic1', '72.ij1', '72.ik1', '108.y1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 87178291200, 40297548, 36933], 'label': '6912.ia.36.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567634
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.j1', '18.bo1'], 'contains': ['72.z1', '72.ba1', '72.bb1', '72.hu1', '72.hv1', '72.hz1', '72.ib1', '108.ba1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.36.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567635
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.i1', '18.bo1'], 'contains': ['72.y1', '72.ba1', '72.bc1', '72.hs1', '72.ht1', '72.hy1', '72.ia1', '108.z1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 87178291200, 36933, 87100665, 83480268], 'label': '6912.ia.36.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567636
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.i1', '18.bp1'], 'contains': ['72.ba1', '72.bd1', '72.bf1', '72.hw1', '72.hx1', '72.id1', '72.ie1', '108.bb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 93405312000, 87178291200, 40297548, 36933], 'label': '6912.ia.36.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567637
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '18.j1', '18.l1', '18.bl1'], 'contains': ['72.x1', '72.z1', '72.bg1', '72.hd1', '72.hk1', '72.if1', '72.ig1', '108.bc1'], 'core': '144.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567638
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.bz1', '12.cb1', '12.cd1', '12.ch1', '12.cj1', '12.da1', '12.dc1', '18.bq1', '18.bx1', '24.du1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36933, 43909226, 47537280, 40279680, 127370880, 87265400268, 93405312000, 127380345, 7620480], 'label': '6912.ia.6.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.z1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567639
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.h1', '18.j1', '18.bp1'], 'contains': ['72.ba1', '72.be1', '72.bg1', '72.hl1', '72.hm1', '72.ih1', '72.ii1', '108.bd1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567640
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '12.bo1', '18.bj1'], 'contains': ['72.i1', '72.j1', '72.n1', '72.r1', '72.ja1', '72.jb1', '72.jc1', '72.bl1', '72.bm1', '72.cn1', '72.cs1', '72.jf1', '72.jh1', '72.jq1', '72.kg1', '72.qh1', '72.qk1', '108.eu1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gp1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567641
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.bj1', '18.bk1', '18.bl1'], 'contains': ['72.k1', '72.l1', '72.x1', '72.bh1', '72.ja1', '72.jd1', '72.je1', '72.bn1', '72.bo1', '72.ct1', '72.cu1', '72.jk1', '72.jl1', '72.kh1', '72.ki1', '108.ev1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567642
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '18.bj1'], 'contains': ['72.m1', '72.o1', '72.s1', '72.t1', '72.jb1', '72.jc1', '72.je1', '72.co1', '72.cp1', '72.cv1', '72.cw1', '72.jv1', '72.jx1', '72.kp1', '72.kq1', '108.ew1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gr1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567643
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '18.bj1', '18.bm1', '18.bn1'], 'contains': ['72.p1', '72.q1', '72.u1', '72.jb1', '72.jd1', '72.cq1', '72.cr1', '72.cx1', '72.ju1', '72.ka1', '72.kr1', '108.ex1'], 'core': '144.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gs1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567644
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '18.bj1', '18.bo1', '18.bp1'], 'contains': ['72.v1', '72.w1', '72.ba1', '72.jc1', '72.jd1', '72.cy1', '72.cz1', '72.da1', '72.ks1', '72.kt1', '72.kw1', '108.ey1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gt1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567645
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '18.bl1', '18.bm1', '18.bo1'], 'contains': ['72.z1', '72.y1', '72.bi1', '72.jd1', '72.je1', '72.dc1', '72.db1', '72.dj1', '72.la1', '72.lb1', '72.lg1', '108.ez1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 36933, 83480268, 40279680], 'label': '6912.ia.36.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gu1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567646
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '18.bk1', '18.bn1', '18.bo1'], 'contains': ['72.bb1', '72.bc1', '72.jd1', '72.dd1', '72.de1', '72.lc1', '72.ld1', '108.fa1'], 'core': '144.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.36.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567647
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.bk1', '18.bm1', '18.bp1'], 'contains': ['72.bd1', '72.be1', '72.jd1', '72.df1', '72.dg1', '72.le1', '72.lf1', '108.fb1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87178291200, 36933, 119769548, 40279680], 'label': '6912.ia.36.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567648
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1'], 'contains': ['72.mk1', '72.mm1', '72.mo1', '72.mq1', '72.mr1', '72.my1', '72.na1', '72.nl1', '72.nn1', '72.nv1', '72.nx1', '72.ph1', '72.pj1', '72.py1', '72.qa1', '108.gh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.36.jz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567649
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.c1'], 'contains': ['12.c1', '12.bz1', '12.cc1', '12.ci1', '12.ck1', '12.db1', '12.dd1', '18.br1', '18.by1', '24.dv1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.ba1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.ba1', 'subgroup_fusion': None, 'weyl_group': '384.20051'}
  • id: 243567650
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dq1', '12.ds1', '18.f1'], 'contains': ['72.mk1', '72.mn1', '72.mp1', '72.mr1', '72.ms1', '72.mz1', '72.nb1', '72.nm1', '72.no1', '72.nw1', '72.ny1', '72.pi1', '72.pk1', '72.pz1', '72.qb1', '108.gi1'], 'core': '144.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87178291200, 36933, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.36.ka1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ka1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567651
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1'], 'contains': ['72.ml1', '72.mm1', '72.mn1', '72.mt1', '72.mv1', '72.my1', '72.mz1', '72.nq1', '72.ns1', '72.ob1', '72.od1', '72.ps1', '72.pu1', '72.qc1', '72.qe1', '108.gj1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.36.kb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567652
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '18.f1'], 'contains': ['72.ml1', '72.mo1', '72.mp1', '72.mv1', '72.mw1', '72.na1', '72.nb1', '72.nr1', '72.nt1', '72.oc1', '72.oe1', '72.pt1', '72.pv1', '72.qd1', '72.qf1', '108.gk1'], 'core': '144.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 87178291200, 36933, 83463146], 'label': '6912.ia.36.kc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567653
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '18.y1', '18.m1', '18.n1'], 'contains': ['72.ci1', '72.cm1', '72.im1', '108.bk1', '144.u1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87218570880, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567654
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1'], 'contains': ['72.bl1', '72.bm1', '72.bo1', '72.bp1', '72.br1', '72.bu1', '72.bw1', '72.cp1', '72.cq1', '72.cv1', '72.cy1', '72.do1', '72.ds1', '72.ey1', '72.fk1', '108.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87091200, 36933, 43909226, 93405312000, 87305662080, 127380345, 7620480], 'label': '6912.ia.36.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567655
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1', '18.o1', '18.p1'], 'contains': ['72.bl1', '72.bn1', '72.bq1', '72.bs1', '72.by1', '72.co1', '72.cr1', '72.cz1', '72.dp1', '72.dw1', '72.fy1', '108.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 87218607813, 93405312000, 36933, 87100665], 'label': '6912.ia.36.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567656
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1', '18.q1', '18.r1'], 'contains': ['72.bm1', '72.bn1', '72.bt1', '72.bv1', '72.bx1', '72.cw1', '72.cx1', '72.da1', '72.ew1', '72.fa1', '72.fo1', '108.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.36.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567657
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bl1', '18.o1', '18.q1'], 'contains': ['72.bn1', '72.bo1', '72.bz1', '72.cf1', '72.ch1', '72.dh1', '72.dc1', '72.dj1', '72.hk1', '72.ic1', '72.ik1', '108.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 87218570880, 40312609, 93405312000, 40297548, 36933], 'label': '6912.ia.36.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567658
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1', '18.p1', '18.q1'], 'contains': ['72.bn1', '72.cb1', '72.ce1', '72.dd1', '72.df1', '72.ho1', '72.hr1', '108.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.36.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567659
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1', '18.o1', '18.r1'], 'contains': ['72.bn1', '72.cc1', '72.cd1', '72.de1', '72.dg1', '72.hp1', '72.hq1', '108.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 87218607813, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.36.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567660
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.ca1', '12.cb1', '12.cc1', '12.ct1', '12.cv1', '12.dg1', '12.di1', '18.bt1', '18.bz1', '24.dx1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 47537280, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.6.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bb1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567661
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '18.bl1', '18.p1', '18.r1'], 'contains': ['72.bn1', '72.ca1', '72.cg1', '72.db1', '72.di1', '72.hn1', '72.ig1', '108.bk1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.36.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567662
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.o1', '18.bq1'], 'contains': ['72.bs1', '72.bz1', '72.cd1', '72.dv1', '72.ea1', '72.fz1', '72.gd1', '72.nm1', '72.nn1', '72.nr1', '72.ns1', '108.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.36.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567663
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.p1', '18.bq1'], 'contains': ['72.bs1', '72.ca1', '72.ce1', '72.dz1', '72.eb1', '72.gc1', '72.ge1', '108.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.36.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567664
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.o1', '18.br1'], 'contains': ['72.bs1', '72.cc1', '72.cf1', '72.dy1', '72.ec1', '72.gb1', '72.gf1', '108.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 40297548, 7621226, 36933], 'label': '6912.ia.36.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567665
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.f1', '18.p1', '18.br1'], 'contains': ['72.bs1', '72.cb1', '72.cg1', '72.dx1', '72.ed1', '72.ga1', '72.gg1', '72.nl1', '72.no1', '72.nq1', '72.nt1', '108.bo1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87109068, 93405312000, 87124129, 7620480, 32929, 7621226], 'label': '6912.ia.36.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243567666
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.a1', '18.m1', '18.bs1'], 'contains': ['72.ci1', '72.ee1', '72.gh1', '72.np1', '72.nu1', '108.bo1', '144.x1'], 'core': '144.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 32929, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567667
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.q1', '18.bq1'], 'contains': ['72.bv1', '72.bz1', '72.ce1', '72.fb1', '72.ff1', '72.hl1', '72.hy1', '108.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.36.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567668
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.r1', '18.bq1'], 'contains': ['72.bv1', '72.ca1', '72.cd1', '72.fe1', '72.fg1', '72.hw1', '72.hz1', '108.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.36.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567669
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.q1', '18.br1'], 'contains': ['72.bv1', '72.cb1', '72.cf1', '72.fd1', '72.fh1', '72.hu1', '72.id1', '108.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 43909226, 93405312000, 40297548, 36933], 'label': '6912.ia.36.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567670
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '18.h1', '18.r1', '18.br1'], 'contains': ['72.bv1', '72.cc1', '72.cg1', '72.fc1', '72.fi1', '72.hs1', '72.ih1', '108.bs1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87109068, 93405312000, 87124129, 7620480, 32929], 'label': '6912.ia.36.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567671
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.c1'], 'contains': ['12.c1', '12.ca1', '12.cd1', '12.cu1', '12.cw1', '12.dh1', '12.dj1', '18.bu1', '18.ca1', '24.dy1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.bc1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bc1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567672
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '18.b1', '18.n1', '18.bs1'], 'contains': ['72.ci1', '72.fj1', '72.in1', '108.bs1', '144.z1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 43909226, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567673
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.q1', '18.bt1'], 'contains': ['72.bx1', '72.bz1', '72.cb1', '72.fn1', '72.fs1', '72.gt1', '72.gx1', '72.nw1', '72.nx1', '72.oc1', '72.od1', '108.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.36.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567674
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.r1', '18.bt1'], 'contains': ['72.bx1', '72.ca1', '72.cc1', '72.fr1', '72.ft1', '72.gw1', '72.gy1', '108.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.36.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567675
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.q1', '18.bu1'], 'contains': ['72.bx1', '72.ce1', '72.cf1', '72.fq1', '72.fu1', '72.gv1', '72.gz1', '108.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 40297548, 36933, 87185912426], 'label': '6912.ia.36.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567676
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '18.f1', '18.r1', '18.bu1'], 'contains': ['72.bx1', '72.cd1', '72.cg1', '72.fp1', '72.fv1', '72.gu1', '72.ha1', '72.nv1', '72.ny1', '72.ob1', '72.oe1', '108.bw1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.36.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567677
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '18.a1', '18.n1', '18.bv1'], 'contains': ['72.ci1', '72.fw1', '72.hb1', '72.nz1', '72.of1', '108.bw1', '144.bb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87185912426, 2676, 87124129, 87109068], 'label': '6912.ia.36.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567678
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '18.bw1'], 'contains': ['72.cj1', '72.fx1', '72.hc1', '72.oa1', '72.og1', '108.bw1', '144.bc1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 32929, 36933, 87185912426, 93405314676, 87124129, 87109068], 'label': '6912.ia.36.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '36.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567679
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.o1', '18.bt1'], 'contains': ['72.by1', '72.bz1', '72.cc1', '72.gj1', '72.gn1', '72.hm1', '72.ia1', '108.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.36.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567680
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.p1', '18.bt1'], 'contains': ['72.by1', '72.ca1', '72.cb1', '72.gm1', '72.go1', '72.hx1', '72.ib1', '108.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.36.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567681
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.o1', '18.bu1'], 'contains': ['72.by1', '72.cd1', '72.cf1', '72.gl1', '72.gp1', '72.hv1', '72.ie1', '108.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 93405312000, 87222200426, 40297548, 36933], 'label': '6912.ia.36.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567682
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['3456.h1', '3456.c1', '3456.f1', '3456.m1', '3456.j1', '3456.l1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.f1', '6.c1', '6.x1', '6.ba1', '8.e1', '8.l1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 40312609, 36933, 43909226, 47537280, 40279680, 127370880, 87109068, 93405312000, 7620480], 'label': '6912.ia.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.f1', '6.c1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243567683
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.d1', '12.cx1', '12.dl1', '18.bv1', '18.ca1', '24.br1', '24.dz1'], 'core': '12.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 40312609, 36933, 47537280, 40279680, 87222200426, 127370880, 87109068, 7620480], 'label': '6912.ia.6.bd1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bd1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567684
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.h1', '18.p1', '18.bu1'], 'contains': ['72.by1', '72.ce1', '72.cg1', '72.gk1', '72.gq1', '72.ht1', '72.ii1', '108.ca1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.36.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567685
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.b1', '18.m1', '18.bv1'], 'contains': ['72.ci1', '72.gr1', '72.io1', '108.ca1', '144.be1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 32929, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567686
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.bw1'], 'contains': ['72.cj1', '72.gs1', '72.iq1', '108.ca1', '144.bf1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 32929, 87222200426, 36933, 93405314676, 87124129, 87109068], 'label': '6912.ia.36.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '36.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567687
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '18.be1', '18.m1', '18.s1'], 'contains': ['72.cm1', '72.ee1', '72.gr1', '72.ol1', '72.on1', '108.cg1', '144.bk1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 40280426, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.36.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567688
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '18.y1', '18.s1', '18.t1'], 'contains': ['72.cm1', '72.ef1', '72.il1', '108.cl1', '144.bl1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567689
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '18.be1', '18.n1', '18.t1'], 'contains': ['72.cm1', '72.fj1', '72.fw1', '72.om1', '72.on1', '108.cp1', '144.bm1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 40297548, 36933, 87265400268, 2676, 40279680], 'label': '6912.ia.36.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567690
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '18.bf1', '18.m1', '18.t1'], 'contains': ['72.cm1', '72.gh1', '72.io1', '108.ct1', '144.bn1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 32929, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567691
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '18.bf1', '18.n1', '18.s1'], 'contains': ['72.cm1', '72.hb1', '72.in1', '108.cx1', '144.bo1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87218570880, 43909226, 32929, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567692
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1'], 'contains': ['72.cn1', '72.co1', '72.cq1', '72.cs1', '72.cu1', '72.cw1', '72.cy1', '72.dk1', '72.dm1', '72.dn1', '72.dr1', '72.eh1', '72.ej1', '72.ex1', '72.fl1', '108.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 87305662080, 93405312000, 36933, 119750400, 87091200], 'label': '6912.ia.36.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567693
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1', '18.u1', '18.v1'], 'contains': ['72.cn1', '72.cp1', '72.cr1', '72.ct1', '72.da1', '72.dl1', '72.dq1', '72.dt1', '72.du1', '72.el1', '72.gi1', '108.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 93405312000, 43945413, 36933, 87100665], 'label': '6912.ia.36.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567694
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1'], 'contains': ['12.ce1', '12.cy1', '12.dn1', '18.bw1', '18.ca1', '24.bs1', '24.ea1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40312609, 36933, 47537280, 40279680, 87222200426, 127370880, 93525427956, 87109068, 7620480], 'label': '6912.ia.6.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1', 'old_label': '6.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.be1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567695
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bn1', '18.o1', '18.u1'], 'contains': ['72.cr1', '72.dh1', '72.de1', '72.dv1', '72.ec1', '72.gj1', '72.gp1', '72.op1', '72.oq1', '72.ox1', '72.oz1', '108.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 93405312000, 40297548, 36933, 746], 'label': '6912.ia.36.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567696
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bm1', '18.o1', '18.v1'], 'contains': ['72.cr1', '72.dc1', '72.dg1', '72.dy1', '72.ea1', '72.gl1', '72.gn1', '108.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 93405312000, 36933, 87100665, 119769548], 'label': '6912.ia.36.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567697
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bm1', '18.p1', '18.u1'], 'contains': ['72.cr1', '72.db1', '72.df1', '72.dx1', '72.eb1', '72.gk1', '72.go1', '108.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 36933, 87100665, 83480268, 83481548], 'label': '6912.ia.36.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567698
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '18.bn1', '18.p1', '18.v1'], 'contains': ['72.cr1', '72.dd1', '72.di1', '72.dz1', '72.ed1', '72.gm1', '72.gq1', '72.oq1', '72.os1', '72.oy1', '72.pa1', '108.cg1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.36.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567699
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bj1', '18.w1', '18.x1'], 'contains': ['72.cs1', '72.ct1', '72.cv1', '72.cx1', '72.cz1', '72.eg1', '72.ei1', '72.ek1', '72.ev1', '72.ez1', '72.fm1', '108.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 93405312000, 43945413, 36933, 87100665], 'label': '6912.ia.36.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567700
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bl1', '18.u1', '18.w1'], 'contains': ['72.ct1', '72.cu1', '72.dh1', '72.db1', '72.dj1', '72.em1', '72.es1', '72.eu1', '72.hd1', '72.hj1', '72.ij1', '108.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 93405312000, 43908480, 40297548, 36933], 'label': '6912.ia.36.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567701
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1', '18.v1', '18.w1'], 'contains': ['72.ct1', '72.dd1', '72.dg1', '72.eo1', '72.er1', '72.hf1', '72.hi1', '108.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 43945413, 36933, 87100665, 119769548], 'label': '6912.ia.36.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567702
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1', '18.u1', '18.x1'], 'contains': ['72.ct1', '72.de1', '72.df1', '72.ep1', '72.eq1', '72.hg1', '72.hh1', '108.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 43945413, 36933, 87100665, 83481548], 'label': '6912.ia.36.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567703
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '18.bl1', '18.v1', '18.x1'], 'contains': ['72.ct1', '72.dc1', '72.di1', '72.en1', '72.et1', '72.he1', '72.if1', '108.cl1'], 'core': '288.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87218570880, 93405312000, 32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.36.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dg1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567704
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bn1', '18.q1', '18.w1'], 'contains': ['72.cx1', '72.dh1', '72.dd1', '72.fb1', '72.fh1', '72.fn1', '72.fu1', '72.ot1', '72.ou1', '72.ox1', '72.oy1', '108.co1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 93405312000, 40280426, 40297548, 36933], 'label': '6912.ia.36.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567705
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.cg1', '12.ch1', '12.ci1', '12.cq1', '12.cs1', '12.dg1', '12.dh1', '18.cb1', '18.cd1', '24.ef1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 47537280, 36933, 87265400268, 83480268, 119769548, 40279680], 'label': '6912.ia.6.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bf1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567706
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bm1', '18.q1', '18.x1'], 'contains': ['72.cx1', '72.dc1', '72.df1', '72.fd1', '72.ff1', '72.fq1', '72.fs1', '108.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 93405312000, 36933, 87100665, 83481548], 'label': '6912.ia.36.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.di1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567707
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bm1', '18.r1', '18.w1'], 'contains': ['72.cx1', '72.db1', '72.dg1', '72.fc1', '72.fg1', '72.fp1', '72.ft1', '108.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 93405312000, 36933, 87100665, 83480268, 119769548], 'label': '6912.ia.36.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dh1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567708
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '18.bn1', '18.r1', '18.x1'], 'contains': ['72.cx1', '72.de1', '72.di1', '72.fe1', '72.fi1', '72.fr1', '72.fv1', '72.ou1', '72.ow1', '72.oz1', '72.pa1', '108.cp1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 40297548, 36933, 87265400268, 40279680], 'label': '6912.ia.36.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dk1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567709
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bp1', '18.o1', '18.w1'], 'contains': ['72.cz1', '72.dh1', '72.dg1', '72.fz1', '72.gf1', '72.hm1', '72.ie1', '108.cs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 93405312000, 40297548, 7621226, 36933], 'label': '6912.ia.36.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567710
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1', '18.o1', '18.x1'], 'contains': ['72.cz1', '72.dc1', '72.de1', '72.gb1', '72.gd1', '72.hv1', '72.ia1', '108.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 87218607813, 93405312000, 36933, 87100665], 'label': '6912.ia.36.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567711
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1', '18.p1', '18.w1'], 'contains': ['72.cz1', '72.db1', '72.dd1', '72.ga1', '72.ge1', '72.ht1', '72.ib1', '108.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 87218607813, 93405312000, 36933, 87100665, 83480268], 'label': '6912.ia.36.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567712
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '18.bp1', '18.p1', '18.x1'], 'contains': ['72.cz1', '72.df1', '72.di1', '72.gc1', '72.gg1', '72.hx1', '72.ii1', '108.ct1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87218570880, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.36.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567713
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bp1', '18.q1', '18.u1'], 'contains': ['72.da1', '72.dh1', '72.df1', '72.gt1', '72.gz1', '72.hl1', '72.id1', '108.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43909226, 93405312000, 40297548, 36933], 'label': '6912.ia.36.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567714
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1', '18.q1', '18.v1'], 'contains': ['72.da1', '72.dc1', '72.dd1', '72.gv1', '72.gx1', '72.hu1', '72.hy1', '108.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 87218607813, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.36.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dq1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567715
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1', '18.r1', '18.u1'], 'contains': ['72.da1', '72.db1', '72.de1', '72.gu1', '72.gy1', '72.hs1', '72.hz1', '108.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 87218607813, 43909226, 93405312000, 36933, 87100665, 83480268], 'label': '6912.ia.36.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dp1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567716
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '3.c1'], 'contains': ['12.g1', '12.cg1', '12.cj1', '12.ck1', '12.cr1', '12.di1', '12.dj1', '18.cc1', '18.ce1', '18.cf1', '24.eg1'], 'core': '12.g1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.bg1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bg1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567717
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '18.bp1', '18.r1', '18.v1'], 'contains': ['72.da1', '72.dg1', '72.di1', '72.gw1', '72.ha1', '72.hw1', '72.ih1', '108.cx1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87218570880, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ds1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567718
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.u1', '18.cb1'], 'contains': ['72.dt1', '72.dv1', '72.dx1', '72.em1', '72.eq1', '72.gt1', '72.gu1', '72.pi1', '72.pj1', '72.pt1', '72.pu1', '108.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87265400268, 83480268, 83481548], 'label': '6912.ia.36.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dt1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567719
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.v1', '18.cb1'], 'contains': ['72.dt1', '72.dy1', '72.dz1', '72.en1', '72.er1', '72.gv1', '72.gw1', '108.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.36.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.du1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567720
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.u1', '18.cc1'], 'contains': ['72.dt1', '72.eb1', '72.ec1', '72.ep1', '72.es1', '72.gy1', '72.gz1', '108.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 93405312000, 40297548, 36933, 87185912426], 'label': '6912.ia.36.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567721
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1', '18.f1', '18.v1', '18.cc1'], 'contains': ['72.dt1', '72.ea1', '72.ed1', '72.eo1', '72.et1', '72.gx1', '72.ha1', '72.ph1', '72.pk1', '72.ps1', '72.pv1', '108.db1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567722
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.u1', '18.bq1'], 'contains': ['72.du1', '72.dv1', '72.eb1', '72.hd1', '72.hh1', '72.hl1', '72.hz1', '108.dc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 43945413, 36933, 87100665, 87265400268], 'label': '6912.ia.36.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567723
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.v1', '18.bq1'], 'contains': ['72.du1', '72.dz1', '72.ea1', '72.he1', '72.hi1', '72.hw1', '72.hy1', '108.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 43945413, 36933, 87100665, 87305679948], 'label': '6912.ia.36.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567724
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.u1', '18.br1'], 'contains': ['72.du1', '72.dx1', '72.ec1', '72.hg1', '72.hj1', '72.hs1', '72.id1', '108.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 93405312000, 43908480, 40297548, 36933], 'label': '6912.ia.36.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dz1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567725
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.o1', '18.cb1'], 'contains': ['72.dv1', '72.dw1', '72.dy1', '72.hk1', '72.hm1', '72.hq1', '72.hv1', '108.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.36.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567726
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.p1', '18.cb1'], 'contains': ['72.dw1', '72.dx1', '72.dz1', '72.hn1', '72.hr1', '72.ht1', '72.hx1', '108.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83480268, 83481548, 87305679948], 'label': '6912.ia.36.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eb1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567727
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '3.b1'], 'contains': ['12.e1', '12.z1', '12.bb1', '12.bc1', '12.bg1', '12.cm1', '12.df1', '18.cc1', '18.cg1', '24.ca1'], 'core': '12.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.bh1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bh1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567728
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.o1', '18.cc1'], 'contains': ['72.dw1', '72.ea1', '72.ec1', '72.hp1', '72.ic1', '72.ia1', '72.ie1', '108.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 87222200426, 40297548, 87222199680, 36933], 'label': '6912.ia.36.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ec1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567729
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '18.j1', '18.v1', '18.br1'], 'contains': ['72.du1', '72.dy1', '72.ed1', '72.hf1', '72.hu1', '72.if1', '72.ih1', '108.di1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 43908480, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ed1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243567730
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1', '18.j1', '18.p1', '18.cc1'], 'contains': ['72.dw1', '72.eb1', '72.ed1', '72.ho1', '72.ib1', '72.ig1', '72.ii1', '108.dj1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87222200426, 87222199680, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ee1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567731
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1', '18.a1', '18.s1', '18.cg1'], 'contains': ['72.ee1', '72.ef1', '72.hb1', '72.po1', '72.pp1', '108.db1', '144.cj1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 87185912426, 2676, 87109068, 87124129, 32929], 'label': '6912.ia.36.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ef1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567732
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '18.c1', '18.s1', '18.bs1'], 'contains': ['72.ee1', '72.il1', '72.in1', '108.di1', '144.ck1'], 'core': '144.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43909226, 32929, 43908480, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567733
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1', '18.c1', '18.m1', '18.cg1'], 'contains': ['72.ee1', '72.im1', '72.io1', '108.dj1', '144.cl1'], 'core': '144.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 87222200426, 87222199680, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567734
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1', '18.b1', '18.t1', '18.cg1'], 'contains': ['72.ef1', '72.fj1', '72.io1', '108.dn1', '144.cm1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 32929, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.fj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ei1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567735
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.a1', '18.t1', '18.ch1'], 'contains': ['72.ef1', '72.fw1', '72.gh1', '72.pq1', '72.pr1', '108.dr1', '144.cn1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 2676, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.36.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.fk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ej1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567736
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.b1', '18.s1', '18.ch1'], 'contains': ['72.ef1', '72.gr1', '72.in1', '108.dv1', '144.co1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 2676, 87109068, 87124129, 32929], 'label': '6912.ia.36.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.fl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ek1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567737
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.w1', '18.cb1'], 'contains': ['72.ei1', '72.em1', '72.er1', '72.fb1', '72.fc1', '72.hm1', '72.ht1', '108.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 87265400268, 83480268, 119769548], 'label': '6912.ia.36.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.el1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567738
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '3.a1'], 'contains': ['12.f1', '12.cn1', '12.dl1', '18.ce1', '18.cg1', '24.cb1', '24.ei1'], 'core': '12.f1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87185911680, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.bi1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bi1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567739
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.x1', '18.cb1'], 'contains': ['72.ei1', '72.en1', '72.eq1', '72.fd1', '72.fe1', '72.hv1', '72.hx1', '108.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.36.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.em1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567740
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.w1', '18.cc1'], 'contains': ['72.ei1', '72.eo1', '72.es1', '72.fg1', '72.fh1', '72.ib1', '72.ie1', '108.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 93405312000, 87222200426, 40297548, 36933], 'label': '6912.ia.36.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.en1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567741
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1', '18.h1', '18.x1', '18.cc1'], 'contains': ['72.ei1', '72.ep1', '72.et1', '72.ff1', '72.fi1', '72.ia1', '72.ii1', '108.dn1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 87222200426, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eo1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567742
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '18.w1', '18.ck1'], 'contains': ['72.ek1', '72.em1', '72.eo1', '72.fn1', '72.fp1', '72.fz1', '72.ga1', '72.pz1', '72.qa1', '72.qd1', '72.qe1', '108.do1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 87265400268, 83480268], 'label': '6912.ia.36.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ep1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567743
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.x1', '18.ck1'], 'contains': ['72.ek1', '72.en1', '72.ep1', '72.fq1', '72.fr1', '72.gb1', '72.gc1', '108.dp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.36.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eq1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567744
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.w1', '18.cl1'], 'contains': ['72.ek1', '72.er1', '72.es1', '72.ft1', '72.fu1', '72.ge1', '72.gf1', '108.dq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 93405312000, 40297548, 7621226, 36933], 'label': '6912.ia.36.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.er1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567745
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.f1', '18.x1', '18.cl1'], 'contains': ['72.ek1', '72.eq1', '72.et1', '72.fs1', '72.fv1', '72.gd1', '72.gg1', '72.py1', '72.qb1', '72.qc1', '72.qf1', '108.dr1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.36.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ft1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.es1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567746
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.u1', '18.ck1'], 'contains': ['72.el1', '72.em1', '72.ep1', '72.gj1', '72.gk1', '72.hl1', '72.hs1', '108.ds1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 87265400268, 83480268], 'label': '6912.ia.36.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.et1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567747
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.v1', '18.ck1'], 'contains': ['72.el1', '72.en1', '72.eo1', '72.gl1', '72.gm1', '72.hu1', '72.hw1', '108.dt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 93405312000, 36933, 87100665, 87305679948], 'label': '6912.ia.36.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.eu1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567748
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.u1', '18.cl1'], 'contains': ['72.el1', '72.eq1', '72.es1', '72.go1', '72.gp1', '72.hz1', '72.id1', '108.du1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 87185911680, 43909226, 93405312000, 40297548, 36933], 'label': '6912.ia.36.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ev1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567749
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1'], 'contains': ['12.cl1', '12.co1', '12.dm1', '18.cf1', '18.cg1', '24.cc1', '24.ej1'], 'core': '36.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40312609, 87185911680, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.6.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '6.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bj1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567750
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.h1', '18.v1', '18.cl1'], 'contains': ['72.el1', '72.er1', '72.et1', '72.gn1', '72.gq1', '72.hy1', '72.ih1', '108.dv1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ew1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567751
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '18.w1', '18.bq1'], 'contains': ['72.ez1', '72.fb1', '72.fg1', '72.fz1', '72.ge1', '72.hd1', '72.hi1', '108.dw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 43945413, 36933, 87100665, 87265400268], 'label': '6912.ia.36.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ex1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567752
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.x1', '18.bq1'], 'contains': ['72.ez1', '72.fe1', '72.ff1', '72.gc1', '72.gd1', '72.he1', '72.hh1', '108.dx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 43945413, 36933, 87100665, 87305679948], 'label': '6912.ia.36.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.fz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ey1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567753
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.w1', '18.br1'], 'contains': ['72.ez1', '72.fc1', '72.fh1', '72.ga1', '72.gf1', '72.hf1', '72.hj1', '108.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 40297548, 7621226, 36933], 'label': '6912.ia.36.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ga1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ez1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567754
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '18.l1', '18.x1', '18.br1'], 'contains': ['72.ez1', '72.fd1', '72.fi1', '72.gb1', '72.gg1', '72.hg1', '72.if1', '108.dz1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43908480, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.36.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fa1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567755
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '18.q1', '18.cb1'], 'contains': ['72.fa1', '72.fb1', '72.fd1', '72.gt1', '72.gv1', '72.hk1', '72.hr1', '108.ea1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 93405312000, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.36.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fb1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567756
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.r1', '18.cb1'], 'contains': ['72.fa1', '72.fc1', '72.fe1', '72.gu1', '72.gw1', '72.hn1', '72.hq1', '108.eb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 36933, 87100665, 83480268, 119769548, 87305679948], 'label': '6912.ia.36.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fc1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567757
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.q1', '18.cc1'], 'contains': ['72.fa1', '72.ff1', '72.fh1', '72.gx1', '72.gz1', '72.ho1', '72.ic1', '108.ec1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 87222199680, 36933, 87185912426], 'label': '6912.ia.36.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ge1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fd1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567758
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '18.l1', '18.r1', '18.cc1'], 'contains': ['72.fa1', '72.fg1', '72.fi1', '72.gy1', '72.ha1', '72.hp1', '72.ig1', '108.ed1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87185912426, 87222199680, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fe1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567759
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '18.d1', '18.t1', '18.bs1'], 'contains': ['72.fj1', '72.gh1', '72.il1', '108.dz1', '144.df1'], 'core': '288.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32929, 43908480, 7621226, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.gg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ff1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567760
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '3.a1'], 'contains': ['12.i1', '12.cn1', '12.cx1', '18.ch1', '18.cj1', '24.cd1', '24.el1'], 'core': '12.i1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87185911680, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.bk1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bk1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567761
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '18.d1', '18.n1', '18.cg1'], 'contains': ['72.fj1', '72.hb1', '72.im1', '108.ed1', '144.dg1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87185912426, 87222199680, 2676, 87109068, 87124129, 32929], 'label': '6912.ia.36.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.gh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567762
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.w1', '18.bt1'], 'contains': ['72.fm1', '72.fn1', '72.ft1', '72.hd1', '72.hf1', '72.hm1', '72.ib1', '108.ee1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 87265400268, 119769548], 'label': '6912.ia.36.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fh1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567763
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.x1', '18.bt1'], 'contains': ['72.fm1', '72.fr1', '72.fs1', '72.he1', '72.hg1', '72.hx1', '72.ia1', '108.ef1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 83481548, 87305679948], 'label': '6912.ia.36.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fi1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567764
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.w1', '18.bu1'], 'contains': ['72.fm1', '72.fp1', '72.fu1', '72.hi1', '72.hj1', '72.ht1', '72.ie1', '108.eg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 87222200426, 40297548, 36933], 'label': '6912.ia.36.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fj1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567765
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.q1', '18.ck1'], 'contains': ['72.fn1', '72.fo1', '72.fq1', '72.hk1', '72.hl1', '72.ho1', '72.hu1', '108.eh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 119768268, 43909226, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.36.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fk1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567766
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.r1', '18.ck1'], 'contains': ['72.fo1', '72.fp1', '72.fr1', '72.hn1', '72.hp1', '72.hs1', '72.hw1', '108.ei1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 36933, 87100665, 83480268, 87305679948], 'label': '6912.ia.36.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567767
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.q1', '18.cl1'], 'contains': ['72.fo1', '72.fs1', '72.fu1', '72.hr1', '72.ic1', '72.hy1', '72.id1', '108.ej1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 93405312000, 40297548, 87222199680, 36933], 'label': '6912.ia.36.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fm1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567768
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.j1', '18.x1', '18.bu1'], 'contains': ['72.fm1', '72.fq1', '72.fv1', '72.hh1', '72.hv1', '72.if1', '72.ii1', '108.ek1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43908480, 87222200426, 36933, 87124129, 87109068], 'label': '6912.ia.36.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.go1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fn1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567769
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '18.j1', '18.r1', '18.cl1'], 'contains': ['72.fo1', '72.ft1', '72.fv1', '72.hq1', '72.hz1', '72.ig1', '72.ih1', '108.el1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87222199680, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.36.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fo1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567770
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.c1', '18.t1', '18.bv1'], 'contains': ['72.fw1', '72.il1', '72.io1', '108.ek1', '144.dn1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43908480, 87222200426, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.36.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.gq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fp1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567771
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '3.b1'], 'contains': ['12.h1', '12.bd1', '12.be1', '12.bi1', '12.bj1', '12.cm1', '12.cz1', '18.ch1', '18.cl1', '24.ce1'], 'core': '12.h1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 93405312000, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.6.bl1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bl1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567772
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '18.c1', '18.n1', '18.ch1'], 'contains': ['72.fw1', '72.im1', '72.in1', '108.el1', '144.do1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 87222199680, 2676, 87109068, 87124129, 32929], 'label': '6912.ia.36.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.gr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fq1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567773
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.bw1'], 'contains': ['72.fx1', '72.ip1', '72.iq1', '108.ek1', '144.dp1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [32929, 43908480, 87222200426, 36933, 93405314676, 87124129, 87109068], 'label': '6912.ia.36.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '36.gs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567774
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '18.o1', '18.ck1'], 'contains': ['72.fy1', '72.fz1', '72.gb1', '72.gj1', '72.gl1', '72.hk1', '72.hp1', '108.em1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 119768268, 93405312000, 36933, 87100665, 87265400268], 'label': '6912.ia.36.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fs1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567775
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.p1', '18.ck1'], 'contains': ['72.fy1', '72.ga1', '72.gc1', '72.gk1', '72.gm1', '72.hn1', '72.ho1', '108.en1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 36933, 87100665, 83480268, 87305679948], 'label': '6912.ia.36.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ft1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567776
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.o1', '18.cl1'], 'contains': ['72.fy1', '72.gd1', '72.gf1', '72.gn1', '72.gp1', '72.hq1', '72.ic1', '108.eo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 40297548, 87222199680, 7621226, 36933], 'label': '6912.ia.36.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fu1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567777
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '18.l1', '18.p1', '18.cl1'], 'contains': ['72.fy1', '72.ge1', '72.gg1', '72.go1', '72.gq1', '72.hr1', '72.ig1', '108.ep1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87222199680, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.36.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fv1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567778
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '18.d1', '18.m1', '18.ch1'], 'contains': ['72.gh1', '72.gr1', '72.im1', '108.ep1', '144.dy1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 87222199680, 2676, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.36.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.gx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fw1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567779
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '18.u1', '18.bt1'], 'contains': ['72.gi1', '72.gj1', '72.go1', '72.gt1', '72.gy1', '72.hd1', '72.hg1', '108.eq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 87265400268, 83481548], 'label': '6912.ia.36.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fx1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567780
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.v1', '18.bt1'], 'contains': ['72.gi1', '72.gm1', '72.gn1', '72.gw1', '72.gx1', '72.he1', '72.hf1', '108.er1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 43945413, 36933, 87100665, 119769548, 87305679948], 'label': '6912.ia.36.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.gz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567781
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.u1', '18.bu1'], 'contains': ['72.gi1', '72.gk1', '72.gp1', '72.gu1', '72.gz1', '72.hh1', '72.hj1', '108.es1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 40312609, 93405312000, 43908480, 40297548, 36933, 87185912426], 'label': '6912.ia.36.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ha1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.fz1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567782
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['12.cp1', '12.cq1', '12.cr1', '12.ct1', '12.cu1', '12.da1', '12.db1', '18.ci1', '18.ck1', '24.eo1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 47537280, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.6.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bm1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567783
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '18.l1', '18.v1', '18.bu1'], 'contains': ['72.gi1', '72.gl1', '72.gq1', '72.gv1', '72.ha1', '72.hi1', '72.if1', '108.et1'], 'core': '288.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43908480, 36933, 87185912426, 87124129, 87109068], 'label': '6912.ia.36.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ga1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567784
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '18.d1', '18.s1', '18.bv1'], 'contains': ['72.gr1', '72.hb1', '72.il1', '108.et1', '144.eb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32929, 43908480, 36933, 87185912426, 2676, 87124129, 87109068], 'label': '6912.ia.36.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.hc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gb1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567785
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '18.bw1'], 'contains': ['72.gs1', '72.hc1', '72.ip1', '108.et1', '144.ec1'], 'core': '864.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [32929, 43908480, 36933, 87185912426, 93405314676, 87124129, 87109068], 'label': '6912.ia.36.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '36.hd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gc1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567786
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '18.bj1'], 'contains': ['72.bp1', '72.bq1', '72.bt1', '72.bu1', '72.dn1', '72.dq1', '72.ev1', '72.ex1', '72.jf1', '72.jh1', '72.jl1', '72.ju1', '72.jx1', '72.kp1', '72.ks1', '108.fd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 43909226, 40279680, 127370880, 93405312000, 87305671545, 7620480], 'label': '6912.ia.36.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.he1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gx1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567787
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '18.bj1', '18.bq1', '18.br1'], 'contains': ['72.br1', '72.bs1', '72.bv1', '72.dr1', '72.du1', '72.ez1', '72.jf1', '72.jk1', '72.jv1', '72.ka1', '72.kt1', '108.fe1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 43909226, 40279680, 127370880, 93405312000, 127380345, 7620480], 'label': '6912.ia.36.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gy1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567788
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '18.bj1', '18.bt1', '18.bu1'], 'contains': ['72.bw1', '72.bx1', '72.by1', '72.fl1', '72.fm1', '72.gi1', '72.jh1', '72.jk1', '72.kq1', '72.kr1', '72.kw1', '108.ff1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.36.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.gz1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567789
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '18.bl1', '18.bq1', '18.bt1'], 'contains': ['72.bz1', '72.ca1', '72.ch1', '72.hd1', '72.he1', '72.ij1', '72.jk1', '72.jl1', '72.kz1', '72.lb1', '72.lg1', '108.fg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 36933, 87265400268, 40279680], 'label': '6912.ia.36.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ha1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567790
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.et1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '18.bk1', '18.br1', '18.bt1'], 'contains': ['72.cb1', '72.cc1', '72.hf1', '72.hg1', '72.jk1', '72.lc1', '72.le1', '108.fh1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 36933, 119769548, 40279680], 'label': '6912.ia.36.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243567791
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '18.bk1', '18.bq1', '18.bu1'], 'contains': ['72.cd1', '72.ce1', '72.hh1', '72.hi1', '72.jk1', '72.ld1', '72.lf1', '108.fi1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 93405312000, 36933, 87298060748, 40279680], 'label': '6912.ia.36.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567792
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.bx1', '18.bl1', '18.br1', '18.bu1'], 'contains': ['72.a1', '72.cf1', '72.cg1', '72.hj1', '72.if1', '72.jk1', '72.la1', '108.fj1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.36.hd1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.hk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hd1', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 243567793
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.k1', '3456.g1', '3456.i1', '3456.h1', '3456.c1', '3456.f1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.e1', '4.g1', '6.y1', '6.bc1', '6.bd1', '6.be1', '8.f1', '8.m1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 40312609, 36933, 47537280, 40279680, 87222200426, 127370880, 87109068, 93405312000, 7620480], 'label': '6912.ia.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.e1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243567794
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '6.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '3.c1'], 'contains': ['12.g1', '12.cp1', '12.cs1', '12.cv1', '12.cw1', '12.dc1', '12.dd1', '18.cj1', '18.cl1', '24.ep1'], 'core': '12.g1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.6.bn1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bn1', 'subgroup_fusion': None, 'weyl_group': '1152.157559'}
  • id: 243567795
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.bx1', '18.y1', '18.bs1', '18.bv1'], 'contains': ['72.b1', '72.ci1', '72.il1', '108.fj1', '144.fx1'], 'core': '72.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.he1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.hl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.he1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567796
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1', '12.ce1', '18.bw1'], 'contains': ['72.cj1', '72.ip1', '72.lp1', '108.fj1', '144.fy1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 36933, 93405314676, 87109068, 40279680], 'label': '6912.ia.36.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.y1', 'old_label': '36.hm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hf1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567797
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '18.z1'], 'contains': ['72.jm1', '72.jn1', '72.jp1', '72.jt1', '72.jy1', '72.km1', '72.ku1', '108.fd1', '144.jp1'], 'core': '144.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.36.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '36.hn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hg1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567798
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '18.z1', '18.bx1', '18.by1'], 'contains': ['72.jm1', '72.jo1', '72.jw1', '72.kb1', '72.kv1', '108.fe1', '144.jq1'], 'core': '144.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.36.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.ho1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hh1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567799
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '18.z1', '18.bz1', '18.ca1'], 'contains': ['72.jn1', '72.jo1', '72.kn1', '72.ko1', '72.kx1', '108.ff1', '144.jr1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [36933, 47537280, 40279680, 127370880, 87222200426, 127380345, 7620480], 'label': '6912.ia.36.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.hp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hi1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567800
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '18.bb1', '18.bx1', '18.bz1'], 'contains': ['72.jo1', '72.jp1', '72.lh1', '72.lj1', '72.lo1', '108.fg1', '144.js1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.36.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.hq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hj1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567801
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.ii1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '18.ba1', '18.by1', '18.bz1'], 'contains': ['72.jo1', '72.lk1', '72.lm1', '108.fh1', '144.jt1'], 'core': '144.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.36.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.hr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567802
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '18.ba1', '18.bx1', '18.ca1'], 'contains': ['72.jo1', '72.ll1', '72.ln1', '108.fi1', '144.ju1'], 'core': '144.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.36.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.hs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567803
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1', '18.z1'], 'contains': ['72.jr1', '72.jt1', '72.jw1', '72.kf1', '72.kk1', '72.kn1', '72.ku1', '108.fk1', '144.ku1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 47537280, 36933, 87305671545, 40279680], 'label': '6912.ia.36.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '36.ht1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hm1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567804
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1', '18.bj1'], 'contains': ['72.dk1', '72.dl1', '72.do1', '72.dp1', '72.eg1', '72.eh1', '72.ew1', '72.ey1', '72.jq1', '72.ju1', '72.jv1', '72.kg1', '72.ki1', '72.kq1', '72.ks1', '108.fk1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 119759865, 43909226, 93405312000, 36933, 87305671545, 40279680], 'label': '6912.ia.36.hn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '36.hu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hn1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243567805
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['864.fc1', '864.gg1', '864.gh1', '864.fd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.g1'], 'contains': ['24.b1', '24.c1', '24.d1', '24.cw1', '24.cx1', '24.cy1', '24.cz1', '32.a1', '32.i1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.g1'], 'normal_contains': ['24.b1', '24.c1', '24.d1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '3456.jo', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243567806
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1', '18.bj1', '18.cb1', '18.cc1'], 'contains': ['72.dm1', '72.ds1', '72.dt1', '72.dw1', '72.ei1', '72.fa1', '72.jq1', '72.jx1', '72.ka1', '72.kh1', '72.kw1', '108.fl1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.36.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ho1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567807
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1', '18.z1', '18.cd1', '18.ce1'], 'contains': ['72.jr1', '72.jy1', '72.kb1', '72.kj1', '72.kx1', '108.fl1', '144.ky1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.36.hp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.hw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hp1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567808
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1', '18.cf1'], 'contains': ['72.js1', '72.jz1', '72.kc1', '72.kl1', '72.ky1', '108.fl1', '144.kz1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.36.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '36.hx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hq1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567809
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1', '18.bn1', '18.bq1', '18.cb1'], 'contains': ['72.dv1', '72.dz1', '72.fb1', '72.fe1', '72.ka1', '72.kz1', '72.ld1', '108.fm1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 40280426, 36933, 87265400268, 40279680], 'label': '6912.ia.36.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.hy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hr1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567810
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1', '18.bm1', '18.br1', '18.cb1'], 'contains': ['72.dy1', '72.dx1', '72.fd1', '72.fc1', '72.ka1', '72.la1', '72.le1', '108.fn1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.36.hs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.hz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hs1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567811
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1', '18.bm1', '18.bq1', '18.cc1'], 'contains': ['72.ea1', '72.eb1', '72.ff1', '72.fg1', '72.ka1', '72.lb1', '72.lf1', '108.fo1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87298060748, 87261771468, 40279680], 'label': '6912.ia.36.ht1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ia1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ht1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567812
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.ck1', '18.bn1', '18.br1', '18.cc1'], 'contains': ['72.a1', '72.ec1', '72.ed1', '72.fh1', '72.fi1', '72.ka1', '72.lc1', '108.fp1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 36933, 87109068, 40279680], 'label': '6912.ia.36.hu1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.ib1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hu1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567813
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1', '18.bd1', '18.bx1', '18.cd1'], 'contains': ['72.kb1', '72.lh1', '72.ll1', '108.fm1', '144.lg1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 40280426, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.36.hv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ic1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hv1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567814
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1', '18.bc1', '18.by1', '18.cd1'], 'contains': ['72.kb1', '72.li1', '72.lm1', '108.fn1', '144.lh1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.36.hw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.id1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hw1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567815
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1', '18.bc1', '18.bx1', '18.ce1'], 'contains': ['72.kb1', '72.lj1', '72.ln1', '108.fo1', '144.li1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87298060748, 87261771468, 40279680], 'label': '6912.ia.36.hx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ie1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hx1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567816
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.h1'], 'contains': ['16.a1', '16.b1', '16.d1', '16.p1', '24.a1', '24.bb1', '24.be1', '32.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.8.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567817
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.ck1', '18.bd1', '18.by1', '18.ce1'], 'contains': ['72.c1', '72.kb1', '72.lk1', '108.fp1', '144.lj1'], 'core': '72.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.hy1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.if1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hy1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567818
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1', '18.cf1'], 'contains': ['72.kc1', '72.lq1', '72.ls1', '108.fo1', '144.lk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 93452849280, 36933, 87298060748, 87261771468, 40279680], 'label': '6912.ia.36.hz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '36.ig1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.hz1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567819
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ck1', '12.cl1', '18.cf1'], 'contains': ['72.kc1', '72.lr1', '72.lt1', '108.fp1', '144.ll1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.36.ia1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bg1', 'old_label': '36.ih1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ia1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567820
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cm1', '12.cn1', '12.co1', '18.y1', '18.cg1', '18.ch1'], 'contains': ['72.b1', '72.ef1', '72.im1', '108.fu1', '144.gd1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.ib1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.ii1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ib1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567821
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1', '18.z1', '18.ci1', '18.cj1'], 'contains': ['72.kf1', '72.kj1', '72.km1', '72.ko1', '72.kv1', '108.fq1', '144.lq1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.36.ic1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ij1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ic1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567822
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1', '18.bj1', '18.ck1', '18.cl1'], 'contains': ['72.ej1', '72.ek1', '72.el1', '72.fk1', '72.fo1', '72.fy1', '72.kg1', '72.kh1', '72.kp1', '72.kr1', '72.kt1', '108.fq1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87185911680, 36933, 43909226, 40279680, 127370880, 93405312000, 127380345], 'label': '6912.ia.36.id1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ik1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.id1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567823
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cq1', '18.bl1', '18.cb1', '18.ck1'], 'contains': ['72.em1', '72.en1', '72.eu1', '72.hk1', '72.hn1', '72.ik1', '72.kh1', '72.ki1', '72.kz1', '72.la1', '72.lg1', '108.fr1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.36.ie1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.il1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ie1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567824
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1', '18.bk1', '18.cc1', '18.ck1'], 'contains': ['72.eo1', '72.ep1', '72.ho1', '72.hp1', '72.kh1', '72.lc1', '72.lf1', '108.fs1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93405312000, 36933, 87298060748, 40279680], 'label': '6912.ia.36.if1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.im1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.if1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567825
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1', '18.bk1', '18.cb1', '18.cl1'], 'contains': ['72.eq1', '72.er1', '72.hq1', '72.hr1', '72.kh1', '72.ld1', '72.le1', '108.ft1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93405312000, 36933, 119769548, 40279680], 'label': '6912.ia.36.ig1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.in1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ig1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567826
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.cm1', '18.bl1', '18.cc1', '18.cl1'], 'contains': ['72.a1', '72.es1', '72.et1', '72.ic1', '72.ig1', '72.kh1', '72.lb1', '108.fu1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.36.ih1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.io1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ih1', 'subgroup_fusion': None, 'weyl_group': '576.8659'}
  • id: 243567827
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.h1'], 'contains': ['16.a1', '16.c1', '16.e1', '16.q1', '24.bc1', '24.bf1', '24.bg1', '32.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.8.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567828
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cq1', '18.bb1', '18.cd1', '18.ci1'], 'contains': ['72.kj1', '72.kk1', '72.lh1', '72.li1', '72.lo1', '108.fr1', '144.md1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.36.ii1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ip1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ii1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567829
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1', '18.ba1', '18.ce1', '18.ci1'], 'contains': ['72.kj1', '72.lk1', '72.ln1', '108.fs1', '144.me1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 47537280, 36933, 87298060748, 40279680], 'label': '6912.ia.36.ij1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.iq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ij1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567830
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1', '18.ba1', '18.cd1', '18.cj1'], 'contains': ['72.kj1', '72.ll1', '72.lm1', '108.ft1', '144.mf1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 47537280, 36933, 119769548, 40279680], 'label': '6912.ia.36.ik1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ir1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ik1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567831
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.cn1', '18.bb1', '18.ce1', '18.cj1'], 'contains': ['72.c1', '72.kj1', '72.lj1', '108.fu1', '144.mg1'], 'core': '72.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.il1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.is1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.il1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567832
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1', '18.cf1'], 'contains': ['72.kl1', '72.lr1', '72.ls1', '108.fs1', '144.mh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 87185911680, 93452849280, 36933, 87298060748, 40279680], 'label': '6912.ia.36.im1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '36.it1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.im1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567833
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.co1', '18.cf1'], 'contains': ['72.kl1', '72.lq1', '72.lt1', '108.fu1', '144.mi1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.36.in1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bj1', 'old_label': '36.iu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.in1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243567834
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1', '18.bd1', '18.bz1', '18.ci1'], 'contains': ['72.ko1', '72.lh1', '72.lk1', '108.fv1', '144.mu1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.36.io1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.iv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.io1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567835
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cu1', '18.bc1', '18.ca1', '18.ci1'], 'contains': ['72.ko1', '72.li1', '72.ln1', '108.fw1', '144.mv1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87298060748, 83480268, 40279680], 'label': '6912.ia.36.ip1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.iw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ip1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567836
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1', '18.bc1', '18.bz1', '18.cj1'], 'contains': ['72.ko1', '72.lj1', '72.lm1', '108.fx1', '144.mw1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87261771468, 119769548, 40279680], 'label': '6912.ia.36.iq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ix1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iq1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567837
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cw1', '12.cx1', '12.cy1', '18.bd1', '18.ca1', '18.cj1'], 'contains': ['72.c1', '72.ko1', '72.ll1', '108.fy1', '144.mx1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.36.ir1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.iy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ir1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567838
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.h1'], 'contains': ['16.a1', '16.f1', '16.g1', '16.r1', '24.bd1', '24.bh1', '24.bi1', '24.bj1', '32.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 43909226, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.8.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567839
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1', '18.bn1', '18.bt1', '18.ck1'], 'contains': ['72.fn1', '72.fr1', '72.gj1', '72.gm1', '72.kr1', '72.kz1', '72.lc1', '108.fv1'], 'core': '288.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 127390028, 93405312000, 36933, 87265400268, 40279680], 'label': '6912.ia.36.is1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.iz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.is1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567840
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cu1', '18.bm1', '18.bu1', '18.ck1'], 'contains': ['72.fq1', '72.fp1', '72.gl1', '72.gk1', '72.kr1', '72.la1', '72.lf1', '108.fw1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87298060748, 83480268, 40279680], 'label': '6912.ia.36.it1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ja1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.it1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567841
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1', '18.bm1', '18.bt1', '18.cl1'], 'contains': ['72.fs1', '72.ft1', '72.gn1', '72.go1', '72.kr1', '72.lb1', '72.le1', '108.fx1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87261771468, 119769548, 40279680], 'label': '6912.ia.36.iu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iu1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567842
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.cw1', '18.bn1', '18.bu1', '18.cl1'], 'contains': ['72.a1', '72.fu1', '72.fv1', '72.gp1', '72.gq1', '72.kr1', '72.ld1', '108.fy1'], 'core': '72.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87218571626, 36933, 87109068, 40279680], 'label': '6912.ia.36.iv1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.jc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iv1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567843
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.cx1', '18.be1', '18.bv1', '18.ch1'], 'contains': ['72.b1', '72.fw1', '72.gr1', '108.fy1', '144.gj1'], 'core': '72.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 87218571626, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.iw1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.jd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567844
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.cy1', '18.bw1'], 'contains': ['72.fx1', '72.gs1', '72.lp1', '108.fy1', '144.gk1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 40312609, 87218571626, 36933, 93405314676, 87109068, 40279680], 'label': '6912.ia.36.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.be1', 'old_label': '36.je1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ix1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567845
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.da1', '18.bp1', '18.bq1', '18.ck1'], 'contains': ['72.fz1', '72.gc1', '72.hl1', '72.hw1', '72.kt1', '72.kz1', '72.lf1', '108.fz1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 36933, 87265400268, 40279680], 'label': '6912.ia.36.iy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iy1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567846
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.db1', '18.bo1', '18.br1', '18.ck1'], 'contains': ['72.gb1', '72.ga1', '72.hu1', '72.hs1', '72.kt1', '72.la1', '72.lc1', '108.ga1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 36933, 83480268, 40279680], 'label': '6912.ia.36.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.iz1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567847
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dc1', '18.bo1', '18.bq1', '18.cl1'], 'contains': ['72.gd1', '72.ge1', '72.hy1', '72.hz1', '72.kt1', '72.lb1', '72.ld1', '108.gb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 93405312000, 36933, 87261771468, 40279680], 'label': '6912.ia.36.ja1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ja1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567848
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cz1', '12.dd1', '12.de1', '18.bp1', '18.br1', '18.cl1'], 'contains': ['72.a1', '72.gf1', '72.gg1', '72.id1', '72.ih1', '72.kt1', '72.le1', '108.gc1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.36.jb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.ji1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jb1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243567849
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.i1'], 'contains': ['16.i1', '16.j1', '16.l1', '24.da1', '24.dd1', '24.dg1', '32.b1'], 'core': '48.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87178291200, 36933, 47537280, 93405312000, 9465, 7620480, 32929], 'label': '6912.ia.8.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567850
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.cz1', '18.bf1', '18.bs1', '18.ch1'], 'contains': ['72.b1', '72.gh1', '72.in1', '108.gc1', '144.gm1'], 'core': '72.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.jc1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.jj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jc1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567851
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.da1', '18.bh1', '18.bx1', '18.ci1'], 'contains': ['72.kv1', '72.lh1', '72.ln1', '108.fz1', '144.nr1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 47537280, 36933, 87265400268, 40279680], 'label': '6912.ia.36.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.jk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jd1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567852
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.db1', '18.bg1', '18.by1', '18.ci1'], 'contains': ['72.kv1', '72.li1', '72.lk1', '108.ga1', '144.ns1'], 'core': '288.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.36.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.jl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.je1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567853
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dc1', '18.bg1', '18.bx1', '18.cj1'], 'contains': ['72.kv1', '72.lj1', '72.ll1', '108.gb1', '144.nt1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.36.jf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.jm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jf1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567854
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.dd1', '18.bh1', '18.by1', '18.cj1'], 'contains': ['72.c1', '72.kv1', '72.lm1', '108.gc1', '144.nu1'], 'core': '72.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.jg1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '36.jn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jg1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567855
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.de1', '18.bi1'], 'contains': ['72.lu1', '108.gc1', '144.go1', '144.nv1', '144.nw1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 43909226, 36933, 87109068, 40279680], 'label': '6912.ia.36.jh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1', 'old_label': '36.jo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jh1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 243567856
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dg1', '18.bp1', '18.bt1', '18.cb1'], 'contains': ['72.gt1', '72.gw1', '72.hm1', '72.hx1', '72.kw1', '72.kz1', '72.le1', '108.gd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.36.ji1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ji1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567857
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dh1', '18.bo1', '18.bu1', '18.cb1'], 'contains': ['72.gv1', '72.gu1', '72.hv1', '72.ht1', '72.kw1', '72.la1', '72.ld1', '108.ge1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 36933, 83480268, 40279680], 'label': '6912.ia.36.jj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jj1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567858
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.di1', '18.bo1', '18.bt1', '18.cc1'], 'contains': ['72.gx1', '72.gy1', '72.ia1', '72.ib1', '72.kw1', '72.lb1', '72.lc1', '108.gf1'], 'core': '288.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 93405312000, 87222200426, 36933, 87261771468, 40279680], 'label': '6912.ia.36.jk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.jr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jk1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567859
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.df1', '12.dj1', '12.dk1', '18.bp1', '18.bu1', '18.cc1'], 'contains': ['72.a1', '72.gz1', '72.ha1', '72.ie1', '72.ii1', '72.kw1', '72.lf1', '108.gg1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.36.jl1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '36.js1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jl1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243567860
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.i1'], 'contains': ['16.i1', '16.k1', '16.m1', '24.e1', '24.db1', '24.di1', '32.c1'], 'core': '24.e1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 93405312000, 32929, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.8.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567861
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.df1', '12.dl1', '12.dm1', '18.bf1', '18.bv1', '18.cg1'], 'contains': ['72.b1', '72.hb1', '72.io1', '108.gg1', '144.gq1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87222200426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.36.jm1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.jt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jm1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567862
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dg1', '18.bh1', '18.bz1', '18.cd1'], 'contains': ['72.kx1', '72.lh1', '72.lm1', '108.gd1', '144.ou1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 47537280, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.36.jn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ju1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jn1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567863
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dh1', '18.bg1', '18.ca1', '18.cd1'], 'contains': ['72.kx1', '72.li1', '72.ll1', '108.ge1', '144.ov1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 47537280, 36933, 83480268, 40279680], 'label': '6912.ia.36.jo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.jv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jo1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567864
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.di1', '18.bg1', '18.bz1', '18.ce1'], 'contains': ['72.kx1', '72.lj1', '72.lk1', '108.gf1', '144.ow1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 47537280, 36933, 87261771468, 40279680], 'label': '6912.ia.36.jp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.jw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jp1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567865
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dj1', '12.dl1', '12.dn1', '18.bh1', '18.ca1', '18.ce1'], 'contains': ['72.c1', '72.kx1', '72.ln1', '108.gg1', '144.ox1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87222200426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.36.jq1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.jx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jq1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567866
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.df1', '12.dn1', '12.do1', '18.bw1'], 'contains': ['72.hc1', '72.iq1', '72.lp1', '108.gg1', '144.gs1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40312609, 87222200426, 36933, 93405314676, 87109068, 40279680], 'label': '6912.ia.36.jr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1', 'old_label': '36.jy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jr1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567867
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.di1', '18.cf1'], 'contains': ['72.ky1', '72.lq1', '72.lr1', '108.gf1', '144.oz1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 127380345, 87222200426, 93452849280, 36933, 87261771468, 40279680], 'label': '6912.ia.36.js1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '36.jz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.js1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567868
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dj1', '12.dm1', '12.do1', '18.cf1'], 'contains': ['72.ky1', '72.ls1', '72.lt1', '108.gg1', '144.pa1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40312609, 87222200426, 93452849280, 36933, 87109068, 40279680], 'label': '6912.ia.36.jt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.cf1', 'old_label': '36.ka1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jt1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567869
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dk1', '12.dl1', '12.do1', '18.bi1'], 'contains': ['72.lu1', '108.gg1', '144.gu1', '144.pb1', '144.pc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [120116474, 127370880, 40312609, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.36.ju1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bi1', 'old_label': '36.kb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ju1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 243567870
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dk1', '12.dm1', '12.dn1', '12.do1'], 'contains': ['72.lv1', '108.gg1', '144.gv1', '144.pd1', '144.pe1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 93525428474, 40312609, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.36.jv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jv1', 'old_label': '36.kc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.jv1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 243567871
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.i1'], 'contains': ['16.i1', '16.n1', '16.o1', '24.dc1', '24.dk1', '24.dm1', '24.dn1', '32.d1'], 'core': '48.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87178291200, 36933, 47537280, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.8.k1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567872
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dt1', '18.a1'], 'contains': ['72.nd1', '72.np1', '72.of1', '72.ol1', '72.oo1', '72.po1', '72.pr1', '108.gm1', '144.io1'], 'core': '144.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 7621226, 36933, 2676, 87265382400], 'label': '6912.ia.36.kd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.kd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567873
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.du1', '18.a1'], 'contains': ['72.nd1', '72.nu1', '72.nz1', '72.om1', '72.oo1', '72.pp1', '72.pq1', '108.go1', '144.ip1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 36933, 2676, 83463146, 87265382400], 'label': '6912.ia.36.ke1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.ke1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ke1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243567874
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1'], 'contains': ['72.nf1', '72.nh1', '72.nj1', '72.nm1', '72.nl1', '72.oc1', '72.ob1', '72.op1', '72.or1', '72.pc1', '72.pe1', '72.pi1', '72.ph1', '72.qd1', '72.qc1', '108.gl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 87124129, 87109068, 87265382400], 'label': '6912.ia.36.kf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.kf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567875
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dt1', '18.f1'], 'contains': ['72.nf1', '72.ni1', '72.nk1', '72.nn1', '72.no1', '72.od1', '72.oe1', '72.or1', '72.os1', '72.pd1', '72.pf1', '72.pj1', '72.pk1', '72.qe1', '72.qf1', '108.gm1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [36933, 87265382400, 9465, 93405312000, 7620480, 32929, 7621226], 'label': '6912.ia.36.kg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.kg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kg1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567876
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1'], 'contains': ['72.ng1', '72.nh1', '72.ni1', '72.nr1', '72.nq1', '72.nw1', '72.nv1', '72.ot1', '72.ov1', '72.pc1', '72.pd1', '72.pt1', '72.ps1', '72.pz1', '72.py1', '108.gn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 83463146, 87124129, 87109068, 87265382400], 'label': '6912.ia.36.kh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.kh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.kh1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567877
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '36.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.du1', '18.f1'], 'contains': ['72.ng1', '72.nj1', '72.nk1', '72.ns1', '72.nt1', '72.nx1', '72.ny1', '72.ov1', '72.ow1', '72.pe1', '72.pf1', '72.pu1', '72.pv1', '72.qa1', '72.qb1', '108.go1'], 'core': '288.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 83463146, 87265382400], 'label': '6912.ia.36.ki1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.ki1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ki1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243567878
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.bf1', '24.bi1', '24.bk1', '24.bl1'], 'contains': ['96.a1', '96.c1', '144.a1', '144.fu1', '192.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.48.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1', 'normal_contained_in': ['12.b1', '24.a1'], 'normal_contains': ['96.a1', '96.c1', '144.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567879
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': ['144.rj1', '144.rc1', '144.rd1', '144.rf1', '144.rg1'], 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '24.e1', '24.j1', '24.dd1', '24.dj1', '24.dk1'], 'contains': ['96.b1', '144.c1', '144.hn1', '192.d1'], 'core': '48.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 36933, 2676], 'label': '6912.ia.48.d1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.d1', 'normal_contained_in': ['12.a1', '24.e1'], 'normal_contains': ['96.b1', '144.c1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567880
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.a1', '24.bo1', '24.bq1', '24.bt1', '24.bu1'], 'contains': ['96.a1', '96.d1', '144.b1', '144.fw1', '192.h1'], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1', 'normal_contained_in': ['12.c1', '24.a1'], 'normal_contains': ['96.a1', '96.d1', '144.b1'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567881
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.a1', '24.bv1', '24.cf1', '24.cg1', '24.ch1'], 'contains': ['96.a1', '96.e1', '144.ge1', '144.gf1', '144.gg1', '192.s1'], 'core': '48.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.c1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1', 'normal_contained_in': ['12.g1', '24.a1'], 'normal_contains': ['96.a1', '96.e1'], 'normalizer': '1.a1', 'old_label': '48.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567882
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '4.h1'], 'contains': ['16.b1', '16.c1', '16.f1', '16.s1', '24.bm1', '24.bo1', '24.bp1', '32.e1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 43909226, 47537280, 40279680, 127370880, 93405312000, 7620480], 'label': '6912.ia.8.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567883
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': ['144.rj1', '144.rd1', '144.qc1', '144.qg1', '144.qh1'], 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '24.e1', '24.q1', '24.dq1', '24.eb1', '24.eh1'], 'contains': ['96.b1', '144.d1', '144.lf1', '192.m1'], 'core': '48.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 746, 2676], 'label': '6912.ia.48.e1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.e1', 'normal_contained_in': ['12.e1', '24.e1'], 'normal_contains': ['96.b1', '144.d1'], 'normalizer': '1.a1', 'old_label': '48.e1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567884
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': ['144.qc1', '144.qg1', '144.qh1', '144.rf1', '144.rg1', '144.rc1'], 'conjugacy_class_count': 1, 'contained_in': ['16.m1', '24.e1', '24.t1', '24.ds1', '24.ec1', '24.em1'], 'contains': ['96.b1', '144.nd1', '144.ne1', '144.nf1', '192.x1'], 'core': '48.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 2676, 87178291946], 'label': '6912.ia.48.f1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.f1', 'normal_contained_in': ['12.h1', '24.e1'], 'normal_contains': ['96.b1'], 'normalizer': '1.a1', 'old_label': '48.f1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567885
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.d1', 'complements': ['144.nq1', '144.ot1', '144.oy1', '144.nw1', '144.nv1', '144.pc1', '144.pb1', '144.pe1', '144.pd1', '144.d1', '144.mt1', '144.ne1', '144.oh1', '144.nf1', '144.oi1'], 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '24.a1', '24.et1'], 'contains': ['96.c1', '96.d1', '96.e1', '144.qc1', '144.qm1', '192.ce1'], 'core': '48.g1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 87178291200, 7657413, 47537280, 40279680], 'label': '6912.ia.48.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.g1', 'normal_contained_in': ['24.a1'], 'normal_contains': ['96.c1', '96.d1', '96.e1'], 'normalizer': '1.a1', 'old_label': '48.g1', 'projective_image': '6912.ia', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.3', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567886
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '16.a1', '24.bb1', '24.bc1', '24.bd1'], 'contains': ['96.v1', '96.ed1', '144.ft1', '144.fu1', '144.fv1', '192.c1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.48.bk1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567887
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '12.dp1', '16.h1'], 'contains': ['96.z1', '96.ba1', '96.bb1', '96.bs1', '96.bu1', '96.ci1', '96.cl1', '96.ee1', '144.hg1', '144.hi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 120115956, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.48.cq1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cq1', 'old_label': '48.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567888
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '16.i1', '24.da1', '24.db1', '24.dc1'], 'contains': ['96.di1', '144.hn1', '144.hr1', '144.hs1', '192.c1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.48.cr1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '48.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567889
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '24.f1', '24.g1', '24.be1'], 'contains': ['96.f1', '96.bc1', '96.g1', '96.j1', '96.bm1', '96.ef1', '96.dm1', '144.e1', '144.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567890
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '24.f1', '24.h1', '24.bg1'], 'contains': ['96.f1', '96.bf1', '96.bg1', '96.i1', '96.l1', '96.by1', '96.bz1', '96.eg1', '96.dn1', '144.f1', '144.l1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 40280426, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.48.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567891
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '24.g1', '24.i1', '24.bg1'], 'contains': ['96.f1', '96.bg1', '96.k1', '96.n1', '96.ca1', '96.eh1', '96.do1', '144.g1', '144.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 40310618, 87096887, 40279680], 'label': '6912.ia.48.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567892
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '24.f1', '24.i1', '24.bh1'], 'contains': ['96.f1', '96.bh1', '96.m1', '96.o1', '96.cb1', '96.ei1', '96.dp1', '144.h1', '144.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567893
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '4.h1'], 'contains': ['16.b1', '16.e1', '16.g1', '16.t1', '24.bn1', '24.bq1', '24.br1', '24.bs1', '32.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 40279680, 87222200426, 127370880, 93405312000, 7620480], 'label': '6912.ia.8.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567894
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '24.h1', '24.i1', '24.be1'], 'contains': ['96.f1', '96.p1', '96.q1', '96.ej1', '144.i1', '144.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.48.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567895
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '24.g1', '24.h1', '24.bh1'], 'contains': ['96.f1', '96.r1', '96.s1', '96.ek1', '144.j1', '144.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 93405312000, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.48.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567896
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '16.a1', '24.be1', '24.bg1', '24.bh1'], 'contains': ['96.f1', '96.h1', '96.t1', '96.dw1', '96.el1', '144.a1', '144.ft1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.48.bl1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567897
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '16.a1', '24.bj1'], 'contains': ['96.u1', '96.em1', '144.a1', '144.fv1', '192.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.48.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '48.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567898
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dq1', '16.h1', '24.f1'], 'contains': ['96.bc1', '96.bf1', '96.bh1', '96.bn1', '96.bp1', '96.ch1', '96.cm1', '96.en1', '144.hg1', '144.hu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 7621226, 36933, 2676], 'label': '6912.ia.48.cs1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567899
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dr1', '24.f1'], 'contains': ['96.bc1', '96.bg1', '96.bh1', '96.bo1', '96.bq1', '96.ck1', '96.cn1', '96.eo1', '144.hh1', '144.hv1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 87178291200, 36933, 83468087], 'label': '6912.ia.48.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567900
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '16.h1', '24.de1'], 'contains': ['96.bd1', '96.be1', '96.bi1', '96.br1', '96.bt1', '96.cc1', '96.co1', '96.ep1', '144.hi1', '144.hu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.48.cu1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '48.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567901
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '24.de1', '24.df1', '24.dg1'], 'contains': ['96.bd1', '96.bk1', '96.bl1', '96.bw1', '96.bx1', '96.cp1', '96.cq1', '144.hj1', '144.hw1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.48.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567902
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '24.de1'], 'contains': ['96.be1', '96.bi1', '96.bl1', '96.ce1', '96.cf1', '96.cr1', '96.cs1', '144.hk1', '144.hz1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 87178291200, 47537280, 7621226, 36933, 7629945], 'label': '6912.ia.48.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '48.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567903
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '24.de1', '24.dh1', '24.di1'], 'contains': ['96.be1', '96.bk1', '96.cd1', '96.cg1', '96.ct1', '144.hl1', '144.ia1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.48.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567904
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.k1', '3456.e1', '3456.c1', '3456.f1', '3456.j1', '3456.l1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.g1', '6.bg1', '6.bh1', '6.bi1', '6.bj1', '8.g1', '8.n1'], 'core': '2.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 40312609, 87185911680, 36933, 47537280, 40279680, 87222200426, 127370880, 87109068, 93405312000], 'label': '6912.ia.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243567905
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '4.h1'], 'contains': ['16.c1', '16.d1', '16.g1', '16.u1', '24.bv1', '24.ca1', '24.cb1', '24.cc1', '32.g1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 47537280, 40279680, 87222200426, 127370880, 93405312000], 'label': '6912.ia.8.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567906
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '24.de1', '24.dl1', '24.dm1'], 'contains': ['96.bi1', '96.bk1', '96.cu1', '96.cv1', '96.cw1', '144.hm1', '144.ie1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 79870533, 36933, 83498639], 'label': '6912.ia.48.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cy1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567907
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '24.dg1', '24.dh1', '24.dl1'], 'contains': ['96.bk1', '96.bl1', '96.cy1', '96.cz1', '96.df1', '144.ho1', '144.ih1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 79833600, 36933, 83480268], 'label': '6912.ia.48.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cz1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567908
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.hb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '24.df1', '24.di1', '24.dl1'], 'contains': ['96.bk1', '96.da1', '96.db1', '144.hp1', '144.ii1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 47537280, 34210, 36933], 'label': '6912.ia.48.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.da1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567909
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '24.df1', '24.dh1', '24.dm1'], 'contains': ['96.bk1', '96.dc1', '96.dd1', '144.hq1', '144.ik1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 7654690, 47537280, 36933], 'label': '6912.ia.48.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.db1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567910
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '16.i1', '24.dg1', '24.di1', '24.dm1'], 'contains': ['96.bk1', '96.cx1', '96.de1', '144.c1', '144.hr1'], 'core': '144.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.48.dc1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567911
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '16.i1', '24.dn1'], 'contains': ['96.dg1', '144.c1', '144.hs1', '192.f1'], 'core': '144.c1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [120116474, 9465, 93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.48.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '48.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567912
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '24.do1'], 'contains': ['96.dh1', '144.ht1', '144.in1', '192.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127388748, 93405312000, 87178291200, 36933, 87124129], 'label': '6912.ia.48.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '48.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567913
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '24.be1', '24.k1', '24.l1'], 'contains': ['96.g1', '96.h1', '96.q1', '96.eq1', '144.u1', '144.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.48.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567914
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '24.f1', '24.k1', '24.bm1'], 'contains': ['96.g1', '96.i1', '96.m1', '96.bn1', '96.bo1', '96.er1', '96.dq1', '144.w1', '144.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.48.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567915
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '24.g1', '24.l1', '24.bm1'], 'contains': ['96.g1', '96.k1', '96.r1', '96.es1', '144.y1', '144.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.48.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567916
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '4.h1'], 'contains': ['16.d1', '16.e1', '16.f1', '16.v1', '24.cd1', '24.ce1', '24.cf1', '32.h1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 43909226, 47537280, 40279680, 127370880, 93405312000], 'label': '6912.ia.8.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567917
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '24.f1', '24.l1', '24.bn1'], 'contains': ['96.g1', '96.l1', '96.o1', '96.bp1', '96.bq1', '96.et1', '96.dr1', '144.ba1', '144.bb1', '144.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.48.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567918
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '24.g1', '24.k1', '24.bn1'], 'contains': ['96.g1', '96.n1', '96.s1', '96.eu1', '144.bd1', '144.be1', '144.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.48.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567919
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '24.bg1', '24.k1', '24.n1'], 'contains': ['96.h1', '96.i1', '96.n1', '96.by1', '96.ca1', '96.ev1', '96.ds1', '144.bk1', '144.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87305662080, 93405312000, 40280426, 36933, 2676, 40279680], 'label': '6912.ia.48.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567920
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '24.be1', '24.n1', '24.o1'], 'contains': ['96.h1', '96.j1', '96.p1', '96.ew1', '144.bl1', '144.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.48.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567921
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '24.bg1', '24.l1', '24.o1'], 'contains': ['96.h1', '96.k1', '96.l1', '96.bz1', '96.ca1', '96.ex1', '96.dt1', '144.bm1', '144.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87305662080, 93405312000, 36933, 40310618, 87096887, 40279680], 'label': '6912.ia.48.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567922
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '24.bh1', '24.k1', '24.o1'], 'contains': ['96.h1', '96.m1', '96.s1', '96.ey1', '144.bn1', '144.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 93405312000, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.48.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567923
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '24.bh1', '24.l1', '24.n1'], 'contains': ['96.h1', '96.o1', '96.r1', '96.ez1', '144.bo1', '144.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87218570880, 43909226, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.48.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567924
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1', '24.f1', '24.n1', '24.ca1'], 'contains': ['96.i1', '96.j1', '96.o1', '96.ch1', '96.ck1', '96.fa1', '96.du1', '144.by1', '144.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 93405312000, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.48.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567925
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '24.h1', '24.n1', '24.bm1'], 'contains': ['96.i1', '96.p1', '96.r1', '96.fb1', '144.cd1', '144.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 36933, 2676, 87091200], 'label': '6912.ia.48.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567926
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1', '24.h1', '24.k1', '24.ca1'], 'contains': ['96.i1', '96.q1', '96.s1', '96.fc1', '144.ce1', '144.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 87222200426, 87222199680, 36933, 2676, 87091200], 'label': '6912.ia.48.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567927
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '4.i1'], 'contains': ['16.j1', '16.k1', '16.n1', '24.dq1', '24.dv1', '24.dw1', '32.e1'], 'core': '48.e1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 47537280, 93405312000, 9465, 7620480, 32929, 7621226], 'label': '6912.ia.8.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567928
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1', '24.g1', '24.o1', '24.ca1'], 'contains': ['96.j1', '96.k1', '96.s1', '96.fd1', '144.cm1', '144.cp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 93405312000, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.48.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567929
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '24.f1', '24.o1', '24.ce1'], 'contains': ['96.j1', '96.l1', '96.m1', '96.cm1', '96.cn1', '96.fe1', '96.dv1', '144.cn1', '144.cq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 93405312000, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.48.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567930
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '24.g1', '24.n1', '24.ce1'], 'contains': ['96.j1', '96.n1', '96.r1', '96.ff1', '144.co1', '144.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87185911680, 43909226, 93405312000, 36933, 2676, 87091200], 'label': '6912.ia.48.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567931
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '24.i1', '24.o1', '24.bm1'], 'contains': ['96.k1', '96.m1', '96.p1', '96.fg1', '144.cx1', '144.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.48.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567932
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '24.i1', '24.l1', '24.ca1'], 'contains': ['96.k1', '96.o1', '96.q1', '96.fh1', '144.da1', '144.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 30938, 87222199680, 36933, 87261759287, 87091200], 'label': '6912.ia.48.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567933
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '24.h1', '24.o1', '24.bn1'], 'contains': ['96.l1', '96.p1', '96.s1', '96.fi1', '144.dj1', '144.dn1', '144.dp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 87222200426, 36933, 2676, 87091200], 'label': '6912.ia.48.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567934
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '24.h1', '24.l1', '24.ce1'], 'contains': ['96.l1', '96.q1', '96.r1', '96.fj1', '144.dk1', '144.do1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43909226, 93405312000, 87222199680, 36933, 2676, 87091200], 'label': '6912.ia.48.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567935
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '24.i1', '24.k1', '24.ce1'], 'contains': ['96.m1', '96.n1', '96.q1', '96.fk1', '144.ds1', '144.dy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 30938, 87222199680, 36933, 87091200, 83468087], 'label': '6912.ia.48.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567936
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '24.i1', '24.n1', '24.bn1'], 'contains': ['96.n1', '96.o1', '96.p1', '96.fl1', '144.dz1', '144.eb1', '144.ec1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 43908480, 30938, 36933, 87261759287, 87091200], 'label': '6912.ia.48.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567937
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.j1', '24.m1', '24.p1', '24.q1', '24.r1', '24.s1', '24.t1', '24.u1', '24.v1', '24.w1', '24.x1', '24.y1', '24.z1', '24.ba1'], 'contains': ['96.b1', '144.fc1', '144.fr1', '144.fs1', '192.b1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.48.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567938
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '4.i1'], 'contains': ['16.j1', '16.m1', '16.o1', '24.ds1', '24.dy1', '24.dz1', '24.ea1', '32.f1'], 'core': '48.f1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 36933, 87185912426, 47537280, 93405312000, 9465, 7620480, 32929], 'label': '6912.ia.8.m1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567939
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1', '16.b1', '24.be1', '24.bm1', '24.bn1'], 'contains': ['96.g1', '96.p1', '96.t1', '96.dx1', '96.fm1', '144.fw1', '144.fx1', '144.fy1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.48.bn1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 243567940
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '16.b1', '24.bb1', '24.bp1', '24.br1'], 'contains': ['96.v1', '96.fn1', '144.b1', '144.fx1', '192.i1'], 'core': '144.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 47537280, 36933, 40279680], 'label': '6912.ia.48.bo1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567942
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.bf1', '24.bo1', '24.bv1', '24.bw1', '24.bx1', '24.by1', '24.bz1'], 'contains': ['96.a1', '96.fp1', '144.fz1', '144.ga1', '144.gb1', '192.l1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.48.bq1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '48.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567943
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '16.c1', '24.bg1', '24.bm1', '24.ca1'], 'contains': ['96.i1', '96.k1', '96.t1', '96.dy1', '96.fq1', '144.fz1', '144.gc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 36933, 2676, 40279680], 'label': '6912.ia.48.br1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567944
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '16.c1', '24.bc1', '24.bp1', '24.cb1'], 'contains': ['96.v1', '96.fr1', '144.ga1', '144.gc1', '192.n1'], 'core': '288.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 40280426, 47537280, 36933, 40279680], 'label': '6912.ia.48.bs1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567945
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1', '16.c1', '24.cc1'], 'contains': ['96.w1', '96.fs1', '144.gb1', '144.gc1', '192.o1'], 'core': '864.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 40280426, 36933, 40279680], 'label': '6912.ia.48.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1', 'old_label': '48.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567946
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cm1', '16.d1', '24.be1', '24.ca1', '24.ce1'], 'contains': ['96.j1', '96.q1', '96.t1', '96.dz1', '96.ft1', '144.gd1', '144.ge1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.48.bu1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567947
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1', '16.d1', '24.bb1', '24.cb1', '24.cd1'], 'contains': ['96.v1', '96.fu1', '144.gd1', '144.gf1', '192.q1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 47537280, 36933, 40279680], 'label': '6912.ia.48.bv1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567948
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1', '16.d1', '24.cc1'], 'contains': ['96.w1', '96.fv1', '144.gd1', '144.gg1', '192.r1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87185911680, 36933, 40279680], 'label': '6912.ia.48.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '48.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567949
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '4.i1'], 'contains': ['16.k1', '16.l1', '16.o1', '24.eg1', '24.eh1', '24.ei1', '24.ej1', '32.g1'], 'core': '48.e1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 87185912426, 47537280, 93405312000, 9465, 32929], 'label': '6912.ia.8.n1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567950
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.bf1', '24.bq1', '24.bw1', '24.cf1', '24.ci1', '24.cj1', '24.ck1'], 'contains': ['96.a1', '96.fw1', '144.gh1', '144.gi1', '192.u1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.48.bx1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '48.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567951
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cx1', '16.e1', '24.bc1', '24.br1', '24.cd1'], 'contains': ['96.v1', '96.fx1', '144.gh1', '144.gj1', '192.v1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.48.by1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567952
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cy1', '16.e1', '24.bs1'], 'contains': ['96.x1', '96.fy1', '144.gh1', '144.gk1', '192.w1'], 'core': '288.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93525427956, 127370880, 47537280, 87218571626, 36933, 40279680], 'label': '6912.ia.48.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '48.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567953
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '16.e1', '24.bg1', '24.bn1', '24.ce1'], 'contains': ['96.l1', '96.n1', '96.t1', '96.ea1', '96.fz1', '144.gi1', '144.gj1', '144.gk1'], 'core': '288.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [127370880, 93405312000, 87218571626, 36933, 2676, 40279680], 'label': '6912.ia.48.ca1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243567954
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cz1', '16.f1', '24.bh1', '24.bm1', '24.ce1'], 'contains': ['96.m1', '96.r1', '96.t1', '96.eb1', '96.ga1', '144.gl1', '144.gm1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 36933, 2676, 40279680], 'label': '6912.ia.48.cb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243567955
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '24.bi1', '24.bo1', '24.bx1', '24.cf1', '24.ci1', '24.cl1', '24.cm1'], 'contains': ['96.a1', '96.gb1', '144.gl1', '144.gn1', '192.z1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.cc1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '48.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567956
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.de1', '16.f1', '24.bj1'], 'contains': ['96.u1', '96.gc1', '144.gl1', '144.go1', '192.ba1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 93405312000, 36933, 40279680], 'label': '6912.ia.48.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '48.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567957
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '16.f1', '24.bd1', '24.bp1', '24.cd1'], 'contains': ['96.v1', '96.gd1', '144.gm1', '144.gn1', '144.go1', '192.bb1'], 'core': '288.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 43909226, 47537280, 36933, 40279680], 'label': '6912.ia.48.ce1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567958
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.df1', '16.g1', '24.bh1', '24.bn1', '24.ca1'], 'contains': ['96.o1', '96.s1', '96.t1', '96.ec1', '96.ge1', '144.gp1', '144.gq1', '144.gs1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 36933, 2676, 40279680], 'label': '6912.ia.48.cf1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567959
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '24.bi1', '24.bq1', '24.bv1', '24.by1', '24.cj1', '24.cl1', '24.cn1'], 'contains': ['96.a1', '96.gf1', '144.gp1', '144.gr1', '144.gt1', '192.be1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.48.cg1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '48.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567960
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '4.i1'], 'contains': ['16.l1', '16.m1', '16.n1', '24.el1', '24.em1', '24.ep1', '32.h1'], 'core': '48.f1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 87185911680, 36933, 47537280, 93405312000, 9465, 32929, 7621226], 'label': '6912.ia.8.o1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567961
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dk1', '16.g1', '24.bj1'], 'contains': ['96.u1', '96.gg1', '144.gp1', '144.gu1', '144.gv1', '192.bf1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 127370880, 93405312000, 87222200426, 36933, 40279680], 'label': '6912.ia.48.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '48.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567962
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dl1', '16.g1', '24.bd1', '24.br1', '24.cb1'], 'contains': ['96.v1', '96.gh1', '144.gq1', '144.gr1', '144.gu1', '192.bg1'], 'core': '288.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 127370880, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.48.ci1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567963
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dm1', '16.g1', '24.cc1'], 'contains': ['96.w1', '96.gi1', '144.gq1', '144.gt1', '144.gv1', '192.bh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87222200426, 36933, 40279680], 'label': '6912.ia.48.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '48.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567964
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dn1', '16.g1', '24.bs1'], 'contains': ['96.x1', '96.gj1', '144.gr1', '144.gs1', '144.gv1', '192.bi1'], 'core': '288.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93525427956, 127370880, 87222200426, 47537280, 36933, 40279680], 'label': '6912.ia.48.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '48.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567965
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.do1', '16.g1'], 'contains': ['96.y1', '96.gk1', '144.gs1', '144.gt1', '144.gu1', '144.gv1', '192.bj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 127370880, 87222200426, 93452849280, 36933, 40279680], 'label': '6912.ia.48.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cl1', 'old_label': '48.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 243567966
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.bk1', '24.bt1', '24.bz1', '24.cg1', '24.ck1', '24.cm1', '24.cn1', '24.co1', '24.cp1', '24.cq1', '24.cr1', '24.cs1', '24.ct1', '24.cu1'], 'contains': ['96.a1', '144.gw1', '144.ha1', '144.he1', '192.bk1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '48.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567967
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.bu1', '24.bw1', '24.ch1', '24.cl1', '24.co1', '24.cv1'], 'contains': ['96.a1', '144.gx1', '144.hb1', '192.bl1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87218603809, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '48.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567968
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '24.bt1', '24.bx1', '24.ch1', '24.cj1', '24.cp1', '24.cv1'], 'contains': ['96.a1', '144.gy1', '144.hc1', '192.bm1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43941409, 127370880, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '48.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567969
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '24.bu1', '24.by1', '24.cg1', '24.ci1', '24.cq1', '24.cv1'], 'contains': ['96.a1', '144.gz1', '144.hd1', '144.hf1', '192.bn1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 87222232609, 93405312000, 47537280, 36933, 40279680], 'label': '6912.ia.48.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '48.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567970
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dt1', '24.f1'], 'contains': ['96.bm1', '96.bn1', '96.bq1', '96.by1', '96.cb1', '96.ch1', '96.cn1', '96.gl1', '144.io1', '144.iq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 7621226, 36933, 2676, 87265382400], 'label': '6912.ia.48.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567971
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.h1'], 'contains': ['16.p1', '16.q1', '16.r1', '16.s1', '16.t1', '16.u1', '16.v1', '24.er1', '24.es1', '24.et1', '32.k1'], 'core': '48.g1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [120115956, 7657413, 87178328133, 43909226, 47537280, 40279680, 127370880, 93405312000], 'label': '6912.ia.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '8.p1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243567972
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.du1', '24.f1'], 'contains': ['96.bm1', '96.bo1', '96.bp1', '96.bz1', '96.cb1', '96.ck1', '96.cm1', '96.gm1', '144.ip1', '144.ir1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 6851, 93405312000, 36933, 83468087, 87265382400], 'label': '6912.ia.48.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243567973
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1', '24.dd1', '24.m1', '24.dp1', '24.dq1', '24.dr1', '24.ds1', '24.dt1'], 'contains': ['96.b1', '144.jl1', '144.jn1', '144.jo1', '192.g1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 36933, 2676], 'label': '6912.ia.48.dh1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567974
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '24.de1'], 'contains': ['96.br1', '96.bt1', '96.bx1', '96.cd1', '96.cf1', '96.cr1', '96.cu1', '144.iv1', '144.jp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [7620480, 93405312000, 47537280, 7621226, 36933, 87178300665], 'label': '6912.ia.48.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '48.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.di1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567975
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '24.de1', '24.du1', '24.dv1'], 'contains': ['96.br1', '96.bw1', '96.ce1', '96.cg1', '96.cv1', '144.ix1', '144.jq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.48.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dj1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567976
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '24.de1', '24.dx1', '24.dy1'], 'contains': ['96.bt1', '96.bw1', '96.cs1', '96.ct1', '96.cw1', '144.jc1', '144.jr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.48.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dk1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567977
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '24.dg1', '24.du1', '24.dx1'], 'contains': ['96.bw1', '96.bx1', '96.cx1', '96.cz1', '96.df1', '144.jf1', '144.js1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 47537280, 36933, 87178300665], 'label': '6912.ia.48.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dl1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567978
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.gj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '24.df1', '24.dv1', '24.dx1'], 'contains': ['96.bw1', '96.da1', '96.dc1', '144.jh1', '144.jt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 7654690, 47537280, 36933], 'label': '6912.ia.48.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243567979
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '24.df1', '24.du1', '24.dy1'], 'contains': ['96.bw1', '96.db1', '96.dd1', '144.jj1', '144.ju1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 47537280, 36933, 87185945890], 'label': '6912.ia.48.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243567980
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '16.j1', '24.dg1', '24.dv1', '24.dy1'], 'contains': ['96.bw1', '96.cy1', '96.de1', '144.jl1', '144.jv1'], 'core': '288.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.48.do1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.do1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243567981
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '16.j1', '24.da1', '24.dw1', '24.dz1'], 'contains': ['96.di1', '144.jn1', '144.jv1', '192.i1'], 'core': '288.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [7620480, 120115956, 9465, 32929, 47537280, 36933], 'label': '6912.ia.48.dp1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567982
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.d1', '18.y1', '18.be1', '18.bf1', '18.m1', '18.n1', '18.s1', '18.t1', '18.bs1', '18.bv1', '18.cg1', '18.ch1', '27.a1', '36.gd1'], 'core': '36.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.9.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243567983
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1', '16.j1', '24.ea1'], 'contains': ['96.dk1', '144.jo1', '144.jv1', '192.j1'], 'core': '864.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [7620480, 93525427956, 9465, 32929, 47537280, 36933], 'label': '6912.ia.48.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '48.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567984
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.p1', '24.dp1', '24.eb1', '24.ec1', '24.ed1', '24.ee1'], 'contains': ['96.b1', '144.jw1', '144.kp1', '192.k1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 87218570880, 93405312000, 32929, 36933, 2676], 'label': '6912.ia.48.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567985
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1', '24.de1'], 'contains': ['96.cc1', '96.cd1', '96.ce1', '96.co1', '96.cq1', '96.cs1', '96.cu1', '144.ku1', '144.kv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 47537280, 7621226, 36933, 7629945, 87178300665], 'label': '6912.ia.48.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.de1', 'old_label': '48.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ds1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243567986
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1', '24.de1', '24.ef1', '24.eg1'], 'contains': ['96.cc1', '96.cf1', '96.cg1', '96.cp1', '96.cw1', '144.kx1', '144.ky1', '144.kz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 47537280, 36933, 87185912426], 'label': '6912.ia.48.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dt1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567987
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1', '24.di1', '24.du1', '24.ef1'], 'contains': ['96.cg1', '96.cx1', '96.db1', '144.lb1', '144.lg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 47537280, 36933, 746], 'label': '6912.ia.48.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.du1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567988
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1', '24.dh1', '24.dv1', '24.ef1'], 'contains': ['96.cg1', '96.cy1', '96.dc1', '144.lc1', '144.lh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.48.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243567989
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1', '24.dh1', '24.du1', '24.eg1'], 'contains': ['96.cg1', '96.cz1', '96.dd1', '144.le1', '144.li1', '144.lk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87261787810, 9465, 93405312000, 79870533, 36933, 87261786529], 'label': '6912.ia.48.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dw1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567990
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ck1', '16.k1', '24.di1', '24.dv1', '24.eg1'], 'contains': ['96.cg1', '96.da1', '96.de1', '144.lf1', '144.lj1', '144.ll1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 47537280, 36933, 746], 'label': '6912.ia.48.dx1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.dx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243567991
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '16.k1', '24.db1', '24.dw1', '24.ei1'], 'contains': ['96.di1', '144.d1', '144.lj1', '192.n1'], 'core': '144.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 32929, 47537280, 36933, 746], 'label': '6912.ia.48.dy1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.dy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dy1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567992
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cl1', '16.k1', '24.ej1'], 'contains': ['96.dj1', '144.d1', '144.ll1', '192.o1'], 'core': '144.d1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [174404119680, 93525427956, 9465, 32929, 36933, 746], 'label': '6912.ia.48.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '48.dz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243567993
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.c1'], 'contains': ['18.z1', '18.ba1', '18.bb1', '18.bc1', '18.bd1', '18.bg1', '18.bh1', '18.bx1', '18.by1', '18.bz1', '18.ca1', '18.cd1', '18.ce1', '18.ci1', '18.cj1', '27.a1', '36.jy1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.9.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 243567994
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1', '24.dd1', '24.r1', '24.dp1', '24.eh1', '24.ek1', '24.em1', '24.en1'], 'contains': ['96.b1', '144.lm1', '144.mb1', '192.p1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 36933, 2676], 'label': '6912.ia.48.ea1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.ea1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ea1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567995
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cn1', '16.l1', '24.da1', '24.ei1', '24.el1'], 'contains': ['96.di1', '144.lm1', '144.mg1', '192.q1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 87185911680, 32929, 47537280, 36933], 'label': '6912.ia.48.eb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '48.eb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567996
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.co1', '16.l1', '24.ej1'], 'contains': ['96.dj1', '144.lm1', '144.mi1', '192.r1'], 'core': '288.d1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 87185911680, 36933, 93525427956, 9465, 32929], 'label': '6912.ia.48.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '48.ec1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243567997
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cp1', '24.de1', '24.eo1', '24.ep1'], 'contains': ['96.co1', '96.cp1', '96.cr1', '96.ct1', '96.cv1', '144.lq1', '144.ls1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 47537280, 7621226, 36933], 'label': '6912.ia.48.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ed1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ed1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567998
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cq1', '24.dg1', '24.ef1', '24.eo1'], 'contains': ['96.cp1', '96.cq1', '96.cx1', '96.cy1', '96.df1', '144.lv1', '144.md1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [93405312000, 32929, 79833600, 36933, 83480268, 87178300665], 'label': '6912.ia.48.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ee1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243567999
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cr1', '24.df1', '24.eg1', '24.eo1'], 'contains': ['96.cp1', '96.da1', '96.dd1', '144.lx1', '144.me1', '144.mh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 47537280, 36933, 87185945890], 'label': '6912.ia.48.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ef1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ef1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568000
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.dk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cs1', '24.df1', '24.ef1', '24.ep1'], 'contains': ['96.cp1', '96.db1', '96.dc1', '144.lz1', '144.mf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 7654690, 47537280, 36933], 'label': '6912.ia.48.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.eg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568001
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '16.l1', '24.dg1', '24.eg1', '24.ep1'], 'contains': ['96.cp1', '96.cz1', '96.de1', '144.mb1', '144.mg1', '144.mi1'], 'core': '288.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [9465, 87185911680, 93405312000, 32929, 47537280, 36933], 'label': '6912.ia.48.eh1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.eh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eh1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243568002
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '24.q1', '24.s1', '24.dr1', '24.ec1', '24.ed1', '24.ek1'], 'contains': ['96.b1', '144.mq1', '144.mt1', '192.t1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 40280426, 36933, 2676], 'label': '6912.ia.48.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.ei1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ei1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568003
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ct1', '24.di1', '24.dx1', '24.eo1'], 'contains': ['96.ct1', '96.cx1', '96.da1', '144.mu1', '144.mz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 47537280, 34210, 36933], 'label': '6912.ia.48.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ej1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ej1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568004
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1', '3.c1'], 'contains': ['18.e1', '18.f1', '18.g1', '18.h1', '18.i1', '18.j1', '18.k1', '18.l1', '18.bj1', '18.bk1', '18.bl1', '18.bm1', '18.bn1', '18.bo1', '18.bp1', '18.o1', '18.p1', '18.q1', '18.r1', '18.u1', '18.v1', '18.w1', '18.x1', '18.bq1', '18.br1', '18.bt1', '18.bu1', '18.cb1', '18.cc1', '18.ck1', '18.cl1', '27.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 93405312000, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.9.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '9.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243568005
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cu1', '24.dh1', '24.dy1', '24.eo1'], 'contains': ['96.ct1', '96.cy1', '96.dd1', '144.mv1', '144.na1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [87261787810, 9465, 93405312000, 79870533, 36933, 83495329], 'label': '6912.ia.48.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ek1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ek1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568006
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cv1', '24.dh1', '24.dx1', '24.ep1'], 'contains': ['96.ct1', '96.cz1', '96.dc1', '144.mw1', '144.nc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83496610, 87261786529], 'label': '6912.ia.48.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.el1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.el1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568007
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cw1', '16.m1', '24.di1', '24.dy1', '24.ep1'], 'contains': ['96.ct1', '96.db1', '96.de1', '144.mx1', '144.nd1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 47537280, 36933, 87178291946], 'label': '6912.ia.48.em1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.em1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.em1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568008
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cx1', '16.m1', '24.db1', '24.dz1', '24.el1'], 'contains': ['96.di1', '144.mx1', '144.ne1', '192.v1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 32929, 47537280, 36933, 87178291946], 'label': '6912.ia.48.en1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '48.en1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.en1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568009
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cy1', '16.m1', '24.ea1'], 'contains': ['96.dk1', '144.mx1', '144.nf1', '192.w1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93525427956, 9465, 32929, 47537280, 36933, 87178291946], 'label': '6912.ia.48.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ea1', 'old_label': '48.eo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568010
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1', '24.dk1', '24.u1', '24.dq1', '24.dr1', '24.ee1', '24.em1', '24.en1'], 'contains': ['96.b1', '144.nn1', '144.nq1', '192.y1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 7621226, 36933, 2676], 'label': '6912.ia.48.ep1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.ep1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ep1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568011
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.da1', '24.dm1', '24.du1', '24.eo1'], 'contains': ['96.cv1', '96.cx1', '96.dd1', '144.nh1', '144.nr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 79870533, 36933, 83498639], 'label': '6912.ia.48.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.eq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eq1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568012
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.db1', '24.dl1', '24.dv1', '24.eo1'], 'contains': ['96.cv1', '96.cy1', '96.da1', '144.ni1', '144.ns1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.48.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.er1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.er1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568013
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dc1', '24.dl1', '24.du1', '24.ep1'], 'contains': ['96.cv1', '96.cz1', '96.db1', '144.nl1', '144.nt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83498639, 87261786529], 'label': '6912.ia.48.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.es1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.es1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568014
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dd1', '16.n1', '24.dm1', '24.dv1', '24.ep1'], 'contains': ['96.cv1', '96.dc1', '96.de1', '144.nn1', '144.nu1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 47537280, 7621226, 36933], 'label': '6912.ia.48.et1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.et1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.et1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568015
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.c1', '3456.f1', '3456.m1', '3456.g1', '3456.i1', '3456.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.f1', '6.bk1', '6.bl1', '6.bn1', '8.h1', '8.o1'], 'core': '2.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 40312609, 87185911680, 36933, 43909226, 47537280, 40279680, 127370880, 87109068, 93405312000], 'label': '6912.ia.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243568016
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': ['576.gj1', '576.fr1', '576.fs1', '576.gc1', '576.gd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1', '6.o1', '6.t1'], 'contains': ['24.b1', '24.j1', '24.p1', '36.a1', '36.gj1', '48.bl1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.b1'], 'normal_contains': ['24.b1', '36.a1', '48.d1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243568017
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.de1', '16.n1', '24.dn1'], 'contains': ['96.dg1', '144.nn1', '144.nv1', '192.ba1'], 'core': '288.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 36933, 9465, 93405312000, 32929, 7621226], 'label': '6912.ia.48.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dn1', 'old_label': '48.eu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568018
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.de1', '24.do1'], 'contains': ['96.dh1', '144.np1', '144.nw1', '192.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 40297548, 36933, 43548794, 87100665, 83463146], 'label': '6912.ia.48.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '48.ev1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ev1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568019
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '16.n1', '24.dc1', '24.dw1', '24.el1'], 'contains': ['96.di1', '144.nq1', '144.nu1', '144.nv1', '192.bb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 9465, 32929, 47537280, 7621226, 36933], 'label': '6912.ia.48.ew1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '48.ew1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ew1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568020
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '24.t1', '24.v1', '24.dt1', '24.eb1', '24.ed1', '24.en1'], 'contains': ['96.b1', '144.oe1', '144.oh1', '144.oi1', '192.bc1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87218571626, 36933, 2676], 'label': '6912.ia.48.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.ex1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ex1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568021
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1', '24.dk1', '24.w1', '24.ds1', '24.dt1', '24.ee1', '24.eh1', '24.ek1'], 'contains': ['96.b1', '144.oq1', '144.ot1', '144.oy1', '192.bd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 36933, 87185912426, 2676], 'label': '6912.ia.48.ey1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.ey1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ey1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568022
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dg1', '24.dm1', '24.dx1', '24.ef1'], 'contains': ['96.cw1', '96.cx1', '96.dc1', '144.ok1', '144.ou1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 87178324129, 7654690, 47537280, 36933], 'label': '6912.ia.48.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.ez1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568023
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dh1', '24.dl1', '24.dy1', '24.ef1'], 'contains': ['96.cw1', '96.cy1', '96.db1', '144.ol1', '144.ov1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 83495329, 87261789839], 'label': '6912.ia.48.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.fa1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fa1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568024
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.di1', '24.dl1', '24.dx1', '24.eg1'], 'contains': ['96.cw1', '96.cz1', '96.da1', '144.oo1', '144.ow1', '144.oz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 79870533, 36933, 87261789839, 87261786529], 'label': '6912.ia.48.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.fb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fb1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568025
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dj1', '16.o1', '24.dm1', '24.dy1', '24.eg1'], 'contains': ['96.cw1', '96.dd1', '96.de1', '144.oq1', '144.ox1', '144.pa1'], 'core': '288.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.48.fc1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ds1', 'old_label': '48.fc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fc1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 243568026
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dk1', '16.o1', '24.dn1'], 'contains': ['96.dg1', '144.oq1', '144.pb1', '144.pd1', '192.bf1'], 'core': '288.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [120116474, 9465, 93405312000, 32929, 36933, 87185912426], 'label': '6912.ia.48.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dn1', 'old_label': '48.fd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568027
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['576.gg1', '576.gh1', '576.fi1', '576.fk1', '576.fm1', '576.fp1', '576.fn1', '576.fq1', '576.ge1', '576.gf1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.s1', '6.v1'], 'contains': ['24.c1', '24.bk1', '24.co1', '36.a1', '36.gn1', '48.dc1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.c1', '36.a1', '48.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243568028
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dk1', '24.do1'], 'contains': ['96.dh1', '144.os1', '144.pc1', '144.pe1', '192.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93405312000, 40297548, 36933, 43548794, 87100665, 87261754346], 'label': '6912.ia.48.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.do1', 'old_label': '48.fe1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fe1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568029
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dl1', '16.o1', '24.dc1', '24.dz1', '24.ei1'], 'contains': ['96.di1', '144.ot1', '144.ox1', '144.pb1', '192.bg1'], 'core': '288.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.48.ff1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '48.ff1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ff1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568030
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dm1', '16.o1', '24.ej1'], 'contains': ['96.dj1', '144.ot1', '144.pa1', '144.pd1', '192.bh1'], 'core': '288.d1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174404119680, 93525427956, 9465, 32929, 36933, 87185912426], 'label': '6912.ia.48.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ej1', 'old_label': '48.fg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568031
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.dn1', '16.o1', '24.ea1'], 'contains': ['96.dk1', '144.ox1', '144.oy1', '144.pd1', '192.bi1'], 'core': '864.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [93525427956, 9465, 32929, 47537280, 36933, 87185912426], 'label': '6912.ia.48.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ea1', 'old_label': '48.fh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568032
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.do1', '16.o1'], 'contains': ['96.dl1', '144.oy1', '144.pa1', '144.pb1', '144.pd1', '192.bj1'], 'core': '864.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 9465, 32929, 93452849280, 36933, 87185912426], 'label': '6912.ia.48.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.fi1', 'old_label': '48.fi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fi1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 243568033
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '24.bb1', '24.er1'], 'contains': ['96.ed1', '96.fn1', '96.fu1', '144.qb1', '144.qc1', '192.bz1'], 'core': '288.f1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 47537280, 87178328133, 40279680], 'label': '6912.ia.48.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.fj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568034
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.q1', '24.bc1', '24.er1'], 'contains': ['96.ed1', '96.fr1', '96.fx1', '144.qd1', '144.qe1', '192.ca1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 127370880, 40280426, 47537280, 87178328133, 40279680], 'label': '6912.ia.48.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.fk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568035
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '24.bd1', '24.er1'], 'contains': ['96.ed1', '96.gd1', '96.gh1', '144.qf1', '144.qg1', '144.qh1', '192.cb1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 127370880, 43909226, 47537280, 87178328133, 40279680], 'label': '6912.ia.48.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.fl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ft1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568036
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.be1', '24.eq1'], 'contains': ['96.dw1', '96.ef1', '96.ej1', '96.dx1', '96.dz1', '96.eq1', '96.ew1', '144.pi1', '144.pl1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 40316613, 93405312000, 87178291200, 2676, 127407813], 'label': '6912.ia.48.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568037
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bg1', '24.eq1'], 'contains': ['96.dw1', '96.eg1', '96.eh1', '96.dn1', '96.do1', '96.dy1', '96.ea1', '96.ev1', '96.ex1', '96.ds1', '96.dt1', '144.pj1', '144.pm1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 127370880, 93405312000, 40280426, 87178291200, 2676], 'label': '6912.ia.48.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568038
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': ['576.fw1', '576.dm1', '576.do1', '576.gg1', '576.gh1', '576.gf1', '576.ge1', '576.dk1', '576.fu1', '576.dl1', '576.ft1', '576.fv1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.a1', '6.ba1', '6.bc1'], 'contains': ['24.c1', '24.bt1', '24.cp1', '36.b1', '36.hd1', '48.do1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.c1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.c1', '36.b1', '48.b1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '1152.157851'}
  • id: 243568039
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bh1', '24.eq1'], 'contains': ['96.dw1', '96.ei1', '96.ek1', '96.eb1', '96.ec1', '96.ey1', '96.ez1', '144.pk1', '144.pn1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 43909226, 93405312000, 87178291200, 2676, 127407813], 'label': '6912.ia.48.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fo1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568040
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.f1', '24.eq1', '24.es1'], 'contains': ['96.ef1', '96.eg1', '96.ei1', '96.en1', '96.eo1', '96.er1', '96.et1', '96.fa1', '96.fe1', '96.gl1', '96.gm1', '144.px1', '144.qi1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93405312000, 24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.48.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568041
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.g1', '24.eq1', '24.es1'], 'contains': ['96.ef1', '96.eh1', '96.ek1', '96.es1', '96.eu1', '96.fd1', '96.ff1', '144.py1', '144.qj1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 87178328133, 2676, 87091200], 'label': '6912.ia.48.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568042
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.h1', '24.eq1', '24.es1'], 'contains': ['96.eg1', '96.ej1', '96.ek1', '96.fb1', '96.fc1', '96.fi1', '96.fj1', '144.pz1', '144.qk1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 87178328133, 2676, 87091200], 'label': '6912.ia.48.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568043
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.i1', '24.eq1', '24.es1'], 'contains': ['96.eh1', '96.ei1', '96.ej1', '96.fg1', '96.fh1', '96.fk1', '96.fl1', '144.qa1', '144.ql1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 43908480, 24536, 87178328133, 87091200, 83468087], 'label': '6912.ia.48.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568044
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '24.be1', '24.es1'], 'contains': ['96.ef1', '96.ej1', '96.el1', '96.eq1', '96.ew1', '96.fm1', '96.ft1', '144.qb1', '144.qm1'], 'core': '288.e1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87178328133, 2676, 40279680], 'label': '6912.ia.48.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.ft1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568045
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.q1', '24.bf1', '24.et1'], 'contains': ['96.c1', '96.fp1', '96.fw1', '144.qd1', '144.qn1', '192.cf1'], 'core': '96.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178291200, 47537280, 40279680], 'label': '6912.ia.48.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.fu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568046
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.q1', '24.bg1', '24.es1'], 'contains': ['96.eg1', '96.eh1', '96.el1', '96.ev1', '96.ex1', '96.fq1', '96.fz1', '144.qe1', '144.qn1'], 'core': '288.e1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178328133, 2676, 40279680], 'label': '6912.ia.48.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.fv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ga1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568047
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '24.bh1', '24.es1'], 'contains': ['96.ei1', '96.ek1', '96.el1', '96.ey1', '96.ez1', '96.ga1', '96.ge1', '144.qf1', '144.qo1'], 'core': '288.e1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 87178328133, 2676, 40279680], 'label': '6912.ia.48.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.fw1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568048
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.r1', '24.bi1', '24.et1'], 'contains': ['96.c1', '96.gb1', '96.gf1', '144.qg1', '144.qo1', '192.cj1'], 'core': '96.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 47537280, 43944719, 87178328133, 40279680], 'label': '6912.ia.48.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.fx1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568049
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['576.ga1', '576.dt1', '576.gk1', '576.gl1', '576.gi1', '576.gb1', '576.gd1', '576.dr1', '576.fy1', '576.ds1', '576.fx1', '576.fz1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.c1', '6.l1', '6.bd1'], 'contains': ['24.d1', '36.b1', '36.he1', '48.bo1', '48.dp1'], 'core': '12.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.d1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': ['4.b1', '6.c1'], 'normal_contains': ['24.d1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568050
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '24.bj1'], 'contains': ['96.em1', '96.gc1', '96.gg1', '144.qh1', '144.qo1', '192.ck1'], 'core': '288.e1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 93405312000, 87178328133, 40279680], 'label': '6912.ia.48.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bj1', 'old_label': '48.fy1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568051
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.f1'], 'contains': ['96.dm1', '96.dn1', '96.dp1', '96.en1', '96.eo1', '96.dq1', '96.dr1', '96.du1', '96.dv1', '96.gl1', '96.gm1', '144.pf1', '144.pg1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [93405312000, 87178291200, 7657413, 24536, 87128133, 83476887], 'label': '6912.ia.48.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1', 'old_label': '48.fz1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243568052
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bm1', '24.eq1'], 'contains': ['96.dx1', '96.dy1', '96.eb1', '96.er1', '96.es1', '96.fb1', '96.fg1', '144.po1', '144.pp1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 40316613, 43909226, 93405312000, 2676, 127407813], 'label': '6912.ia.48.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.ga1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568053
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bn1', '24.eq1'], 'contains': ['96.dx1', '96.ea1', '96.ec1', '96.et1', '96.eu1', '96.fi1', '96.fl1', '144.pq1', '144.pr1', '144.ps1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 40316613, 93405312000, 87222200426, 2676, 127407813], 'label': '6912.ia.48.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gb1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fo1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568054
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.ca1', '24.eq1'], 'contains': ['96.dy1', '96.dz1', '96.ec1', '96.fa1', '96.fc1', '96.fd1', '96.fh1', '144.pt1', '144.pu1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 87185911680, 93405312000, 87222200426, 2676, 127407813], 'label': '6912.ia.48.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gc1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568055
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.ce1', '24.eq1'], 'contains': ['96.dz1', '96.ea1', '96.eb1', '96.fe1', '96.ff1', '96.fj1', '96.fk1', '144.pv1', '144.pw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40316613, 87185911680, 43909226, 93405312000, 2676, 127407813], 'label': '6912.ia.48.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gd1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568056
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.k1', '24.eq1', '24.es1'], 'contains': ['96.eq1', '96.er1', '96.eu1', '96.ev1', '96.ey1', '96.fc1', '96.fk1', '144.qp1', '144.qr1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 87218607813, 93405312000, 24536, 87091200, 83468087], 'label': '6912.ia.48.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.ge1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ge1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568057
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.l1', '24.eq1', '24.es1'], 'contains': ['96.eq1', '96.es1', '96.et1', '96.ex1', '96.ez1', '96.fh1', '96.fj1', '144.qq1', '144.qs1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [87218607813, 43909226, 93405312000, 7657413, 2676, 87091200], 'label': '6912.ia.48.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gf1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568058
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.n1', '24.eq1', '24.es1'], 'contains': ['96.ev1', '96.ew1', '96.ez1', '96.fa1', '96.fb1', '96.ff1', '96.fl1', '144.qt1', '144.qv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [87218607813, 43909226, 93405312000, 43908480, 2676, 87091200], 'label': '6912.ia.48.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gg1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568059
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.o1', '24.eq1', '24.es1'], 'contains': ['96.ew1', '96.ex1', '96.ey1', '96.fd1', '96.fe1', '96.fg1', '96.fi1', '144.qu1', '144.qw1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [87218607813, 93405312000, 43908480, 24536, 87091200, 83468087], 'label': '6912.ia.48.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gh1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568060
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': ['576.dn1', '576.do1', '576.di1', '576.fs1', '576.gj1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.b1', '6.x1', '6.bh1'], 'contains': ['24.b1', '24.q1', '24.s1', '36.c1', '36.hu1', '48.br1'], 'core': '12.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 40280426, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.e1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1', 'normal_contained_in': ['4.c1', '6.b1'], 'normal_contains': ['24.b1', '36.c1', '48.e1'], 'normalizer': '1.a1', 'old_label': '12.e1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568061
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.s1', '24.bm1', '24.es1'], 'contains': ['96.er1', '96.es1', '96.fb1', '96.fg1', '96.fm1', '96.fq1', '96.ga1', '144.qx1', '144.qy1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 43944719, 2676, 40279680], 'label': '6912.ia.48.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gi1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568062
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.t1', '24.bn1', '24.es1'], 'contains': ['96.et1', '96.eu1', '96.fi1', '96.fl1', '96.fm1', '96.fz1', '96.ge1', '144.qz1', '144.ra1', '144.rb1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87222235919, 2676, 40279680], 'label': '6912.ia.48.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gj1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568063
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.s1', '24.bo1', '24.et1'], 'contains': ['96.d1', '96.fp1', '96.gb1', '144.qx1', '144.rc1', '192.dj1'], 'core': '96.d1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 7657413, 47537280, 40279680], 'label': '6912.ia.48.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.gk1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568064
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.s1', '24.bp1', '24.er1'], 'contains': ['96.fn1', '96.fr1', '96.gd1', '144.qy1', '144.rc1', '192.dk1'], 'core': '288.f1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 47537280, 43944719, 40279680], 'label': '6912.ia.48.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.gl1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568065
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.t1', '24.bq1', '24.et1'], 'contains': ['96.d1', '96.fw1', '96.gf1', '144.qz1', '144.rd1', '192.dl1'], 'core': '96.d1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 7657413, 87222200426, 47537280, 40279680], 'label': '6912.ia.48.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.gm1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568066
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.t1', '24.br1', '24.er1'], 'contains': ['96.fn1', '96.fx1', '96.gh1', '144.ra1', '144.rd1', '192.dm1'], 'core': '288.f1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 47537280, 87222235919, 40279680], 'label': '6912.ia.48.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.gn1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568067
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.t1', '24.bs1'], 'contains': ['96.fo1', '96.fy1', '96.gj1', '144.rb1', '144.rd1', '192.dn1'], 'core': '288.f1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [7620480, 93525427956, 127370880, 47537280, 87222235919, 40279680], 'label': '6912.ia.48.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bs1', 'old_label': '48.go1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.go1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568068
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.u1', '24.bv1', '24.et1'], 'contains': ['96.e1', '96.fp1', '96.gf1', '144.re1', '144.rf1', '144.rg1', '192.ds1'], 'core': '96.e1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 93405312000, 87222200426, 47537280, 87185948613, 40279680], 'label': '6912.ia.48.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.gp1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568069
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1', '24.ca1', '24.es1'], 'contains': ['96.fa1', '96.fc1', '96.fd1', '96.fh1', '96.fq1', '96.ft1', '96.ge1', '144.re1', '144.rh1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 87222235919, 2676, 40279680], 'label': '6912.ia.48.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gq1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568070
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1', '24.cb1', '24.er1'], 'contains': ['96.fr1', '96.fu1', '96.gh1', '144.rf1', '144.rh1', '192.du1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 127370880, 47537280, 87185948613, 87222235919, 40279680], 'label': '6912.ia.48.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.gr1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568071
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['576.ga1', '576.dt1', '576.dq1', '576.fg1', '576.fl1', '576.fo1', '576.fn1', '576.fq1', '576.gl1', '576.gk1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.c1', '6.m1', '6.bi1'], 'contains': ['24.d1', '36.c1', '36.hy1', '48.bs1', '48.dy1'], 'core': '12.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 40280426, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.f1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1', 'normal_contained_in': ['4.c1', '6.c1'], 'normal_contains': ['24.d1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.f1', 'projective_image': '3456.jo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568072
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1', '24.cc1'], 'contains': ['96.fs1', '96.fv1', '96.gi1', '144.rg1', '144.rh1', '192.dv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [174404119680, 93525427956, 127370880, 87185911680, 87222235919, 40279680], 'label': '6912.ia.48.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1', 'old_label': '48.gs1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568073
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1', '24.cd1', '24.er1'], 'contains': ['96.fu1', '96.fx1', '96.gd1', '144.ri1', '144.rj1', '192.dx1'], 'core': '576.c1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [120115956, 127370880, 87185911680, 47537280, 43944719, 40279680], 'label': '6912.ia.48.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '48.gt1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568074
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1', '24.ce1', '24.es1'], 'contains': ['96.fe1', '96.ff1', '96.fj1', '96.fk1', '96.ft1', '96.fz1', '96.ga1', '144.ri1', '144.rk1'], 'core': '576.b1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [127370880, 87185911680, 93405312000, 43944719, 2676, 40279680], 'label': '6912.ia.48.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '48.gu1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568075
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '48.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.v1', '24.cf1', '24.et1'], 'contains': ['96.e1', '96.fw1', '96.gb1', '144.rj1', '144.rk1', '192.ea1'], 'core': '96.e1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 47537280, 87185948613, 40279680], 'label': '6912.ia.48.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1', 'old_label': '48.gv1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568076
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '27.a1'], 'contains': ['108.b1', '108.e1', '108.f1', '108.k1', '108.l1', '108.t1', '108.u1', '108.bm1', '108.bn1', '108.bu1', '108.bv1', '108.cz1', '108.da1', '108.dp1', '108.dq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568077
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.f1', '27.a1'], 'contains': ['108.b1', '108.d1', '108.g1', '108.j1', '108.m1', '108.s1', '108.v1', '108.gh1', '108.gi1', '108.gj1', '108.gk1', '108.bl1', '108.bo1', '108.bt1', '108.bw1', '108.cy1', '108.db1', '108.do1', '108.dr1', '108.gl1', '108.gm1', '108.gn1', '108.go1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 32929, 87178291200, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243568078
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '27.a1'], 'contains': ['108.c1', '108.d1', '108.f1', '108.p1', '108.q1', '108.ba1', '108.bb1', '108.bq1', '108.br1', '108.by1', '108.bz1', '108.dl1', '108.dm1', '108.dt1', '108.du1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 40312609, 43909226, 87178291200, 40297548, 36933], 'label': '6912.ia.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568079
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.h1', '27.a1'], 'contains': ['108.c1', '108.e1', '108.g1', '108.o1', '108.r1', '108.z1', '108.bd1', '108.bp1', '108.bs1', '108.bx1', '108.ca1', '108.dk1', '108.dn1', '108.ds1', '108.dv1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 43909226, 32929, 87178291200, 36933, 87124129, 87109068], 'label': '6912.ia.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568080
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '27.a1'], 'contains': ['108.i1', '108.j1', '108.l1', '108.x1', '108.y1', '108.z1', '108.bb1', '108.dd1', '108.de1', '108.dg1', '108.dh1', '108.ef1', '108.eg1', '108.ei1', '108.ej1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43909226, 43908480, 87178291200, 40297548, 36933], 'label': '6912.ia.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568081
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '18.j1', '27.a1'], 'contains': ['108.i1', '108.k1', '108.m1', '108.w1', '108.ba1', '108.bc1', '108.bd1', '108.dc1', '108.df1', '108.di1', '108.dj1', '108.ee1', '108.eh1', '108.ek1', '108.el1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 43908480, 87109068, 87124129, 32929], 'label': '6912.ia.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243568082
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['576.dm1', '576.fw1', '576.do1', '576.fi1', '576.fk1', '576.fp1', '576.fm1', '576.fq1', '576.fn1', '576.dk1', '576.dl1', '576.ft1', '576.fu1', '576.fv1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.a1', '6.bg1', '6.bn1'], 'contains': ['24.c1', '24.cg1', '24.cq1', '36.ih1', '36.il1', '36.in1', '48.eh1'], 'core': '12.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 93405312000, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.g1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.g1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.c1', '48.c1'], 'normalizer': '1.a1', 'old_label': '12.g1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '3456.jo'}
  • id: 243568083
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '27.a1'], 'contains': ['108.n1', '108.o1', '108.q1', '108.s1', '108.u1', '108.w1', '108.y1', '108.dx1', '108.dy1', '108.eb1', '108.ec1', '108.en1', '108.eo1', '108.er1', '108.es1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 40312609, 43908480, 87178291200, 40297548, 7621226, 36933], 'label': '6912.ia.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568084
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '18.l1', '27.a1'], 'contains': ['108.n1', '108.p1', '108.r1', '108.t1', '108.v1', '108.x1', '108.bc1', '108.dw1', '108.dz1', '108.ea1', '108.ed1', '108.em1', '108.ep1', '108.eq1', '108.et1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 87109068, 87124129, 32929, 7621226], 'label': '6912.ia.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568085
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1', '18.bj1', '27.a1'], 'contains': ['108.a1', '108.b1', '108.c1', '108.h1', '108.i1', '108.n1', '108.eu1', '108.ev1', '108.ew1', '108.ex1', '108.ey1', '108.be1', '108.bf1', '108.bg1', '108.cb1', '108.cc1', '108.ch1', '108.fd1', '108.fe1', '108.ff1', '108.fk1', '108.fl1', '108.fq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.54.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568086
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ba1', '18.bk1', '27.a1'], 'contains': ['108.d1', '108.e1', '108.w1', '108.x1', '108.ev1', '108.fa1', '108.fb1', '108.bh1', '108.bi1', '108.ci1', '108.cj1', '108.fh1', '108.fi1', '108.fs1', '108.ft1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 87178291200, 36933, 119769548, 40279680], 'label': '6912.ia.54.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243568087
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.y1', '18.bb1', '18.bl1', '27.a1'], 'contains': ['108.f1', '108.g1', '108.y1', '108.bc1', '108.ev1', '108.ez1', '108.fc1', '108.bj1', '108.bk1', '108.ck1', '108.cl1', '108.fg1', '108.fj1', '108.fr1', '108.fu1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.54.s1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243568088
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bc1', '18.bm1', '27.a1'], 'contains': ['108.k1', '108.j1', '108.p1', '108.o1', '108.ex1', '108.ez1', '108.fb1', '108.ce1', '108.cd1', '108.cn1', '108.cm1', '108.fn1', '108.fo1', '108.fw1', '108.fx1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 87178291200, 36933, 83480268, 119769548, 40279680], 'label': '6912.ia.54.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568089
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bd1', '18.be1', '18.bn1', '27.a1'], 'contains': ['108.l1', '108.m1', '108.q1', '108.r1', '108.ex1', '108.fa1', '108.fc1', '108.cf1', '108.cg1', '108.co1', '108.cp1', '108.fm1', '108.fp1', '108.fv1', '108.fy1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 40280426, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.54.u1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568090
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bg1', '18.bo1', '27.a1'], 'contains': ['108.t1', '108.s1', '108.ba1', '108.z1', '108.ey1', '108.ez1', '108.fa1', '108.cr1', '108.cq1', '108.cv1', '108.cu1', '108.ga1', '108.gb1', '108.ge1', '108.gf1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 87178291200, 36933, 83480268, 40279680], 'label': '6912.ia.54.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568091
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1', '18.bh1', '18.bi1', '18.bp1', '27.a1'], 'contains': ['108.u1', '108.v1', '108.bb1', '108.bd1', '108.ey1', '108.fb1', '108.fc1', '108.cs1', '108.ct1', '108.cw1', '108.cx1', '108.fz1', '108.gc1', '108.gd1', '108.gg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 43909226, 87178291200, 36933, 87109068, 40279680], 'label': '6912.ia.54.w1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568092
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1', '27.a1'], 'contains': ['108.bf1', '108.bj1', '108.bi1', '108.bl1', '108.bn1', '108.bx1', '108.bz1', '108.cf1', '108.ce1', '108.cs1', '108.cr1', '108.df1', '108.dh1', '108.em1', '108.eo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40312609, 36933, 87218570880, 40297548, 7620480, 127388748, 7621226], 'label': '6912.ia.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568093
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': ['576.dn1', '576.do1', '576.di1', '576.fr1', '576.gc1', '576.gd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.b1', '6.y1', '6.bl1'], 'contains': ['24.b1', '24.t1', '24.v1', '36.iv1', '36.iw1', '36.ix1', '48.ca1'], 'core': '12.h1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87218571626, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.12.h1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.h1', 'normal_contained_in': ['4.e1', '6.b1'], 'normal_contains': ['24.b1', '48.f1'], 'normalizer': '1.a1', 'old_label': '12.h1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 243568094
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '18.p1', '27.a1'], 'contains': ['108.bf1', '108.bh1', '108.bk1', '108.bm1', '108.bo1', '108.by1', '108.ca1', '108.cd1', '108.cg1', '108.cq1', '108.ct1', '108.dg1', '108.dj1', '108.en1', '108.ep1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 87218570880, 32929, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568095
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1', '27.a1'], 'contains': ['108.bg1', '108.bj1', '108.bh1', '108.bp1', '108.br1', '108.bt1', '108.bv1', '108.co1', '108.cn1', '108.cw1', '108.cv1', '108.ea1', '108.ec1', '108.eh1', '108.ej1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127388748, 87218570880, 40312609, 43909226, 40297548, 36933], 'label': '6912.ia.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568096
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '18.r1', '27.a1'], 'contains': ['108.bg1', '108.bi1', '108.bk1', '108.bq1', '108.bs1', '108.bu1', '108.bw1', '108.cm1', '108.cp1', '108.cu1', '108.cx1', '108.eb1', '108.ed1', '108.ei1', '108.el1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 32929, 36933, 87124129, 87109068], 'label': '6912.ia.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568097
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1', '27.a1'], 'contains': ['108.cc1', '108.cf1', '108.cd1', '108.ck1', '108.cj1', '108.cw1', '108.cu1', '108.cy1', '108.da1', '108.dc1', '108.de1', '108.ds1', '108.du1', '108.eq1', '108.es1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43909226, 43908480, 40297548, 36933], 'label': '6912.ia.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568098
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1', '18.v1', '27.a1'], 'contains': ['108.cc1', '108.ce1', '108.cg1', '108.ci1', '108.cl1', '108.cv1', '108.cx1', '108.cz1', '108.db1', '108.dd1', '108.di1', '108.dt1', '108.dv1', '108.er1', '108.et1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218570880, 43909226, 32929, 43908480, 36933, 87124129, 87109068], 'label': '6912.ia.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568099
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1', '27.a1'], 'contains': ['108.ch1', '108.ck1', '108.ci1', '108.co1', '108.cm1', '108.cs1', '108.cq1', '108.dk1', '108.dm1', '108.do1', '108.dq1', '108.dw1', '108.dy1', '108.ee1', '108.eg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127388748, 87218570880, 40312609, 43908480, 40297548, 7621226, 36933], 'label': '6912.ia.54.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568100
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1', '18.x1', '27.a1'], 'contains': ['108.ch1', '108.cj1', '108.cl1', '108.cn1', '108.cp1', '108.cr1', '108.ct1', '108.dl1', '108.dn1', '108.dp1', '108.dr1', '108.dx1', '108.dz1', '108.ef1', '108.ek1'], 'core': '864.b1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87218570880, 32929, 43908480, 7621226, 36933, 87124129, 87109068], 'label': '6912.ia.54.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568101
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bq1', '18.bx1', '27.a1'], 'contains': ['108.bl1', '108.bm1', '108.bp1', '108.bq1', '108.dc1', '108.dd1', '108.dw1', '108.dx1', '108.fe1', '108.fg1', '108.fi1', '108.fm1', '108.fo1', '108.fz1', '108.gb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 43909226, 36933, 87265400268, 40279680], 'label': '6912.ia.54.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568102
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.br1', '18.bs1', '18.by1', '27.a1'], 'contains': ['108.bn1', '108.bo1', '108.br1', '108.bs1', '108.de1', '108.di1', '108.dy1', '108.dz1', '108.fe1', '108.fh1', '108.fj1', '108.fn1', '108.fp1', '108.ga1', '108.gc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 43909226, 36933, 87109068, 40279680], 'label': '6912.ia.54.y1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568103
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bt1', '18.bz1', '27.a1'], 'contains': ['108.bt1', '108.bu1', '108.bx1', '108.by1', '108.ee1', '108.ef1', '108.eq1', '108.er1', '108.ff1', '108.fg1', '108.fh1', '108.fv1', '108.fx1', '108.gd1', '108.gf1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 127380345, 36933, 87265400268, 119769548, 40279680], 'label': '6912.ia.54.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.z1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568104
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['576.dq1', '576.fg1', '576.dr1', '576.ds1', '576.fx1', '576.fy1', '576.fz1', '576.gi1', '576.gb1', '576.gd1', '576.fo1', '576.fl1', '576.fq1', '576.fn1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '6.c1', '6.n1', '6.bk1'], 'contains': ['24.d1', '36.jc1', '36.jg1', '36.jh1', '48.ce1', '48.ew1'], 'core': '12.i1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 43909226, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.i1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.i1', 'normal_contained_in': ['4.f1', '6.c1'], 'normal_contains': ['24.d1'], 'normalizer': '1.a1', 'old_label': '12.i1', 'projective_image': '3456.jo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568105
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bu1', '18.bv1', '18.bw1', '18.ca1', '27.a1'], 'contains': ['108.bv1', '108.bw1', '108.bz1', '108.ca1', '108.eg1', '108.ek1', '108.es1', '108.et1', '108.ff1', '108.fi1', '108.fj1', '108.fw1', '108.fy1', '108.ge1', '108.gg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7620480, 127370880, 40312609, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.54.ba1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ba1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568106
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cb1', '18.cd1', '27.a1'], 'contains': ['108.cy1', '108.cz1', '108.df1', '108.dg1', '108.dk1', '108.dl1', '108.ea1', '108.eb1', '108.fl1', '108.fm1', '108.fn1', '108.fr1', '108.ft1', '108.gd1', '108.ge1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 36933, 87265400268, 83480268, 119769548, 40279680], 'label': '6912.ia.54.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bb1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568107
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.cc1', '18.ce1', '18.cf1', '18.cg1', '27.a1'], 'contains': ['108.da1', '108.db1', '108.dh1', '108.dj1', '108.dm1', '108.dn1', '108.ec1', '108.ed1', '108.fl1', '108.fo1', '108.fp1', '108.fs1', '108.fu1', '108.gf1', '108.gg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 87222200426, 36933, 87109068, 40279680], 'label': '6912.ia.54.bc1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bc1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568108
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ci1', '18.ck1', '27.a1'], 'contains': ['108.do1', '108.dp1', '108.ds1', '108.dt1', '108.eh1', '108.ei1', '108.em1', '108.en1', '108.fq1', '108.fr1', '108.fs1', '108.fv1', '108.fw1', '108.fz1', '108.ga1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 127380345, 43909226, 36933, 87265400268, 83480268, 40279680], 'label': '6912.ia.54.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bd1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568109
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '54.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ch1', '18.cj1', '18.cl1', '27.a1'], 'contains': ['108.dq1', '108.dr1', '108.du1', '108.dv1', '108.ej1', '108.el1', '108.eo1', '108.ep1', '108.fq1', '108.ft1', '108.fu1', '108.fx1', '108.fy1', '108.gb1', '108.gc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [127370880, 40312609, 87185911680, 43909226, 36933, 87109068, 40279680], 'label': '6912.ia.54.be1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568110
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.i1', '32.b1', '32.c1', '32.d1'], 'contains': ['128.a1', '128.b1', '192.c1', '192.d1', '192.e1', '192.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 87178291200, 47537280, 36933], 'label': '6912.ia.64.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568111
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.j1', '32.b1', '32.e1', '32.f1'], 'contains': ['128.a1', '128.c1', '192.g1', '192.h1', '192.i1', '192.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 47537280, 36933], 'label': '6912.ia.64.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.b1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568112
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.k1', '32.c1', '32.e1', '32.g1'], 'contains': ['128.a1', '128.d1', '192.l1', '192.m1', '192.n1', '192.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 36933, 746], 'label': '6912.ia.64.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.c1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568113
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '16.l1', '32.b1', '32.g1', '32.h1'], 'contains': ['128.a1', '128.e1', '192.p1', '192.q1', '192.r1', '192.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 87185911680, 93405312000, 47537280, 36933], 'label': '6912.ia.64.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568114
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '16.m1', '32.c1', '32.f1', '32.h1'], 'contains': ['128.a1', '128.f1', '192.u1', '192.v1', '192.w1', '192.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 36933, 87178291946], 'label': '6912.ia.64.e1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568115
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '4.h1'], 'contains': ['24.bb1', '24.bc1', '24.bd1', '24.bp1', '24.br1', '24.cb1', '24.cd1', '24.er1', '36.gd1', '36.ge1', '48.cq1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bl1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '12.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568116
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '16.n1', '32.d1', '32.e1', '32.h1'], 'contains': ['128.a1', '128.g1', '192.y1', '192.z1', '192.ba1', '192.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [43576538, 93405312000, 79833600, 36933, 83468087], 'label': '6912.ia.64.f1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568117
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '16.o1', '32.d1', '32.f1', '32.g1'], 'contains': ['128.a1', '128.h1', '192.bd1', '192.be1', '192.bf1', '192.bg1', '192.bh1', '192.bi1', '192.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [43576538, 93405312000, 79833600, 36933, 87261759287], 'label': '6912.ia.64.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568118
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '32.b1', '32.k1'], 'contains': ['128.b1', '128.c1', '128.e1', '192.bz1', '192.cd1', '192.ce1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [7620480, 120115956, 93405312000, 47537280, 87178328133], 'label': '6912.ia.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.h1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568119
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.q1', '32.c1', '32.k1'], 'contains': ['128.b1', '128.d1', '128.f1', '192.ca1', '192.cf1', '192.cg1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120115956, 93405312000, 47537280, 746, 87178328133], 'label': '6912.ia.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.i1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568120
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '32.d1', '32.k1'], 'contains': ['128.b1', '128.g1', '128.h1', '192.cb1', '192.ci1', '192.cj1', '192.ck1'], 'core': '1152.b1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [43570136, 93405312000, 79833600, 87178328133, 83468087], 'label': '6912.ia.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.j1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568121
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.j1', '32.l1', '32.m1', '32.n1', '32.o1', '32.p1', '32.q1'], 'contains': ['192.a1', '192.cy1', '192.cz1', '192.da1', '192.db1', '192.dc1', '192.dd1', '256.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [120115956, 127370880, 93405312000, 47537280, 40279680], 'label': '6912.ia.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '64.k1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 243568122
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.s1', '32.e1', '32.k1'], 'contains': ['128.c1', '128.d1', '128.g1', '192.df1', '192.dj1', '192.dk1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [7620480, 7656719, 120115956, 93405312000, 47537280], 'label': '6912.ia.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.l1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568123
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.t1', '32.f1', '32.k1'], 'contains': ['128.c1', '128.f1', '128.h1', '192.dh1', '192.dl1', '192.dm1', '192.dn1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120115956, 87185947919, 93405312000, 7657413, 47537280], 'label': '6912.ia.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.m1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568124
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1', '32.g1', '32.k1'], 'contains': ['128.d1', '128.e1', '128.h1', '192.ds1', '192.dt1', '192.du1', '192.dv1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [120115956, 87185947919, 93405312000, 47537280, 87185948613], 'label': '6912.ia.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.n1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568125
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1', '32.h1', '32.k1'], 'contains': ['128.e1', '128.f1', '128.g1', '192.dx1', '192.dy1', '192.ea1'], 'core': '2304.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [7656719, 120115956, 87185911680, 93405312000, 47537280], 'label': '6912.ia.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '64.o1', 'projective_image': '6912.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 243568126
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.c1', '6.l1', '6.m1', '6.n1', '6.bd1', '6.bi1', '6.bk1', '9.a1', '9.b1', '12.bl1', '12.dp1'], 'core': '6.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 120115956, 127370880, 40312609, 43909226, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568127
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.l1', '6.m1', '6.n1'], 'contains': ['24.d1', '36.gj1', '36.gn1', '36.go1', '48.bk1', '48.cr1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [120115956, 127370880, 40312609, 87178291200, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.12.bm1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568128
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': ['96.ee1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.c1', '24.cw1', '36.a1', '36.hd1', '36.hu1', '36.ih1', '36.iv1', '36.jb1', '36.jl1'], 'contains': ['144.fb1', '144.fc1', '144.gw1', '216.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 36933, 87109068, 40279680], 'label': '6912.ia.72.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1', 'normal_contained_in': ['24.b1', '24.c1', '36.a1'], 'normal_contains': ['216.a1', '288.a1', '288.c1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '3456.jo', 'quotient_action_image': '72.46', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568129
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': ['96.ep1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.d1', '24.cx1', '36.c1', '36.gj1', '36.he1', '36.ib1', '36.iw1', '36.jc1', '36.jm1'], 'contains': ['144.fr1', '216.a1', '288.bw1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 36933, 2676, 87109068, 40279680], 'label': '6912.ia.72.b1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.b1', 'normal_contained_in': ['24.b1', '24.d1', '36.c1'], 'normal_contains': ['216.a1', '288.d1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568130
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1', 'complements': ['96.en1', '96.gl1', '96.gm1', '96.eo1'], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.d1', '24.cy1', '36.b1', '36.gn1', '36.hy1', '36.il1', '36.ir1', '36.jg1', '36.jq1'], 'contains': ['144.ha1', '216.a1', '288.hf1'], 'core': '72.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [127370880, 40312609, 47537280, 36933, 87109068, 40279680], 'label': '6912.ia.72.c1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.c1', 'normal_contained_in': ['24.c1', '24.d1', '36.b1'], 'normal_contains': ['216.a1', '288.b1'], 'normalizer': '1.a1', 'old_label': '72.c1', 'projective_image': '3456.jo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 243568131
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '24.f1', '36.gd1'], 'contains': ['144.e1', '144.f1', '144.h1', '144.hg1', '144.hh1', '144.x1', '144.bb1', '144.cj1', '144.cn1', '144.io1', '144.ip1', '144.px1', '144.pf1', '216.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.d1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568132
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '24.g1', '36.gd1'], 'contains': ['144.e1', '144.g1', '144.j1', '144.z1', '144.be1', '144.cm1', '144.co1', '144.py1', '216.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 43909226, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.e1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568133
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '24.h1', '36.gd1'], 'contains': ['144.f1', '144.i1', '144.j1', '144.ck1', '144.cl1', '144.dn1', '144.do1', '144.pz1', '216.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43909226, 43908480, 87178291200, 36933, 2676, 87091200], 'label': '6912.ia.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.f1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568134
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '24.i1', '36.gd1'], 'contains': ['144.g1', '144.h1', '144.i1', '144.df1', '144.dg1', '144.dy1', '144.eb1', '144.qa1', '216.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43908480, 87178291200, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.g1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568135
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.d1', '36.e1', '36.f1', '36.g1', '36.h1', '36.i1', '36.gj1'], 'contains': ['144.hn1', '144.fr1', '144.jw1', '216.z1', '288.g1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40312609, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.h1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568136
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.y1', '24.bb1', '24.be1', '36.gd1'], 'contains': ['144.e1', '144.i1', '144.ft1', '144.u1', '144.bl1', '144.fx1', '144.gd1', '144.pi1', '144.qb1', '216.hn1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 127370880, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.72.ir1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.i1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ir1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 243568137
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.mc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.bb1', '36.ge1', '36.gf1'], 'contains': ['144.b1', '144.fu1', '144.gf1', '144.qc1', '216.hn1', '288.cc1'], 'core': '144.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.72.is1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.j1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.is1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568138
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '4.i1'], 'contains': ['24.da1', '24.db1', '24.dc1', '24.dw1', '24.dz1', '24.ei1', '24.el1', '36.jw1', '36.jy1', '48.cq1'], 'core': '144.d1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [120115956, 87178291200, 36933, 47537280, 9465, 7620480, 32929, 7621226], 'label': '6912.ia.12.dp1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '12.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.dp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568139
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.bf1', '36.ge1', '36.gg1', '36.gh1'], 'contains': ['144.fu1', '144.ga1', '144.gh1', '144.qd1', '216.ho1', '288.cd1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 40280426, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.72.it1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.k1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.it1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568140
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.eh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.be1', '24.bc1', '24.bg1', '36.gd1'], 'contains': ['144.f1', '144.g1', '144.ft1', '144.bk1', '144.bm1', '144.gc1', '144.gj1', '144.pj1', '144.qe1', '216.ho1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [127370880, 40280426, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.72.iu1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1', 'old_label': '72.l1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 243568141
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1', '24.bd1', '24.bh1', '36.gd1'], 'contains': ['144.h1', '144.j1', '144.ft1', '144.bn1', '144.bo1', '144.gm1', '144.gq1', '144.pk1', '144.qf1', '216.hp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [127370880, 43909226, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.72.iv1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568142
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '24.bi1', '36.ge1', '36.gg1', '36.gi1'], 'contains': ['144.fu1', '144.gn1', '144.gr1', '144.qg1', '216.hp1', '288.ch1'], 'core': '288.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.72.iw1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1', 'old_label': '72.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iw1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568143
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bi1', '24.bd1', '24.bj1'], 'contains': ['144.fv1', '144.go1', '144.gu1', '144.qh1', '216.hp1', '288.ci1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [120116474, 127370880, 43909226, 87178291200, 36933, 40279680], 'label': '6912.ia.72.ix1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.ix1', 'old_label': '72.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ix1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568144
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '36.gf1', '36.gh1', '36.gi1', '36.gk1', '36.gl1', '36.gm1', '36.gn1'], 'contains': ['144.fu1', '144.ha1', '144.hb1', '216.hq1', '288.cj1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127370880, 40312609, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.72.iy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iy1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568145
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '36.gf1', '36.gg1', '36.gk1'], 'contains': ['144.fu1', '144.hc1', '144.hd1', '216.hr1', '288.ck1'], 'core': '288.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.72.iz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 243568146
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1', '24.dd1', '36.d1', '36.jw1', '36.jx1'], 'contains': ['144.hn1', '144.jn1', '144.lm1', '216.iy1', '288.cb1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 36933, 2676], 'label': '6912.ia.72.lw1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568147
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1', '24.de1', '36.jy1'], 'contains': ['144.hi1', '144.hj1', '144.hk1', '144.hl1', '144.hm1', '144.jp1', '144.jq1', '144.jr1', '144.ku1', '144.ky1', '144.lq1', '216.it1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.72.lx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568148
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ba1', '24.df1', '36.jy1'], 'contains': ['144.hj1', '144.hp1', '144.hq1', '144.jt1', '144.ju1', '144.me1', '144.mf1', '216.iw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 9465, 87178291200, 7654690, 47537280, 36933], 'label': '6912.ia.72.ly1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ly1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568149
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.e1', '6.o1'], 'contains': ['24.j1', '24.dd1', '24.m1', '24.r1', '24.dp1', '36.d1', '36.p1', '48.h1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87178291200, 36933, 2676, 87124129, 87109068], 'label': '6912.ia.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.m1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568150
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bb1', '24.da1', '24.dg1', '36.jy1'], 'contains': ['144.hj1', '144.ho1', '144.hr1', '144.js1', '144.jv1', '144.md1', '144.mg1', '216.iy1'], 'core': '864.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 9465, 32929, 87178291200, 47537280, 36933], 'label': '6912.ia.72.lz1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.dp1', 'old_label': '72.u1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.lz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568151
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bc1', '24.dh1', '36.jy1'], 'contains': ['144.hl1', '144.ho1', '144.hq1', '144.lh1', '144.li1', '144.mv1', '144.mw1', '216.ja1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 79870533, 36933, 83495329, 83496610], 'label': '6912.ia.72.ma1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.v1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ma1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568152
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bd1', '24.db1', '24.di1', '36.jy1'], 'contains': ['144.hl1', '144.hp1', '144.hr1', '144.lg1', '144.lj1', '144.mu1', '144.mx1', '216.jb1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 47537280, 36933, 746], 'label': '6912.ia.72.mb1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.w1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mb1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 243568153
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.is1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.db1', '36.e1', '36.jw1'], 'contains': ['144.d1', '144.hn1', '144.ne1', '216.jb1', '288.ce1'], 'core': '144.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 36933, 746, 2676], 'label': '6912.ia.72.mc1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.x1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568154
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.hn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.e1', '36.f1', '36.jx1'], 'contains': ['144.hn1', '144.mt1', '144.oh1', '216.jf1', '288.cf1'], 'core': '288.d1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 32929, 40280426, 87178291200, 36933, 2676], 'label': '6912.ia.72.md1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.y1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.md1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568155
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1', '24.dk1', '36.g1', '36.jw1', '36.jx1'], 'contains': ['144.hn1', '144.nq1', '144.ot1', '216.jk1', '288.cg1'], 'core': '288.d1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 7621226, 36933, 2676], 'label': '6912.ia.72.me1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.z1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.me1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568156
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bg1', '24.dl1', '36.jy1'], 'contains': ['144.hm1', '144.ho1', '144.hp1', '144.ns1', '144.nt1', '144.ov1', '144.ow1', '216.ji1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 87178291200, 79870533, 36933, 83498639, 83495329], 'label': '6912.ia.72.mf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.ba1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mf1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568157
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bh1', '24.dc1', '24.dm1', '36.jy1'], 'contains': ['144.hm1', '144.hq1', '144.hr1', '144.nr1', '144.nu1', '144.ou1', '144.ox1', '216.jk1'], 'core': '864.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [9465, 32929, 87178291200, 47537280, 7621226, 36933], 'label': '6912.ia.72.mg1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.jy1', 'old_label': '72.bb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mg1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568158
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bi1', '24.dc1', '24.dn1'], 'contains': ['144.hs1', '144.nv1', '144.pb1', '216.jk1', '288.ci1'], 'core': '864.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [120116474, 9465, 32929, 87178291200, 7621226, 36933], 'label': '6912.ia.72.mh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.mh1', 'old_label': '72.bc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568159
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bi1', '24.do1'], 'contains': ['144.ht1', '144.nw1', '144.pc1', '216.jl1', '288.ci1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [87178291200, 40297548, 36933, 43548794, 87100665, 83463146], 'label': '6912.ia.72.mi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.mi1', 'old_label': '72.bd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 243568160
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.d1', '6.f1'], 'contains': ['24.e1', '24.j1', '24.dj1', '24.q1', '24.t1', '24.eb1', '24.ec1', '36.e1', '36.v1', '48.i1'], 'core': '24.e1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 40280426, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.12.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.n1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568161
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.j1', '36.k1', '36.gp1'], 'contains': ['144.k1', '144.l1', '144.n1', '144.hu1', '144.hv1', '144.w1', '144.ba1', '144.by1', '144.cq1', '144.iq1', '144.ir1', '144.qi1', '144.pg1', '216.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.be1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568162
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.j1', '36.l1', '36.gp1'], 'contains': ['144.k1', '144.m1', '144.t1', '144.y1', '144.bd1', '144.cp1', '144.cr1', '144.qj1', '216.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568163
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.l1', '36.m1', '36.n1', '36.o1', '36.p1', '36.gq1'], 'contains': ['144.k1', '144.o1', '144.r1', '144.hw1', '144.hx1', '144.bg1', '144.bi1', '144.cs1', '144.cu1', '144.is1', '144.it1', '216.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87178291200, 36933, 87124129], 'label': '6912.ia.72.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568164
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.o1', '36.gq1'], 'contains': ['144.k1', '144.q1', '144.s1', '144.bh1', '144.bj1', '144.ct1', '144.cv1', '216.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 93405312000, 87178291200, 40297548, 36933], 'label': '6912.ia.72.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568165
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.q1', '36.gr1'], 'contains': ['144.l1', '144.n1', '144.r1', '144.hz1', '144.ib1', '144.ca1', '144.cc1', '144.dh1', '144.di1', '144.jz1', '144.kb1', '216.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 83471865, 87091200, 83468087], 'label': '6912.ia.72.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bi1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568166
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.q1', '36.r1', '36.gp1'], 'contains': ['144.l1', '144.p1', '144.t1', '144.cd1', '144.ce1', '144.dj1', '144.dk1', '144.qk1', '216.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 43908480, 87178291200, 36933, 87091200], 'label': '6912.ia.72.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568167
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.r1', '36.gr1'], 'contains': ['144.l1', '144.s1', '144.t1', '144.cf1', '144.cg1', '144.dl1', '144.dm1', '216.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 43909226, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.72.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568168
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.q1', '36.gs1'], 'contains': ['144.l1', '144.m1', '144.q1', '144.hy1', '144.id1', '144.cb1', '144.ch1', '144.cw1', '144.dq1', '144.jy1', '144.kc1', '216.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178291200, 36933, 87100665], 'label': '6912.ia.72.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568169
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.r1', '36.t1', '36.s1', '36.u1', '36.v1', '36.gs1'], 'contains': ['144.l1', '144.o1', '144.hy1', '144.ia1', '144.ic1', '144.bz1', '144.ci1', '144.dr1', '144.jx1', '144.ka1', '144.kd1', '216.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.72.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568170
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.q1', '36.w1', '36.gp1'], 'contains': ['144.m1', '144.n1', '144.p1', '144.cx1', '144.da1', '144.ds1', '144.dz1', '144.ql1', '216.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 43908480, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.72.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568171
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.e1', '6.g1'], 'contains': ['24.j1', '24.dj1', '24.s1', '24.v1', '24.ed1', '36.f1', '36.ba1', '48.j1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 127390028, 93405312000, 87178291200, 40297548, 36933, 2676, 40279680], 'label': '6912.ia.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.o1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568172
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.w1', '36.gr1'], 'contains': ['144.m1', '144.n1', '144.s1', '144.cy1', '144.db1', '144.dt1', '144.ea1', '144.ph1', '216.l1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119759865, 93405312000, 87178291200, 36933, 87091200, 83468087], 'label': '6912.ia.72.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bo1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568173
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.q1', '36.gr1'], 'contains': ['144.m1', '144.r1', '144.t1', '144.dc1', '144.dd1', '144.ed1', '144.ee1', '216.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43909226, 93405312000, 87178291200, 36933, 83471865, 87091200], 'label': '6912.ia.72.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.bp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568174
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.w1', '36.y1', '36.x1', '36.z1', '36.ba1', '36.gs1'], 'contains': ['144.m1', '144.o1', '144.ic1', '144.id1', '144.cz1', '144.de1', '144.ef1', '144.ke1', '144.kf1', '216.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 87127439, 40279680], 'label': '6912.ia.72.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568175
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.q1', '36.gt1'], 'contains': ['144.n1', '144.q1', '144.t1', '144.dv1', '144.dw1', '144.eg1', '144.eh1', '216.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127380345, 43909226, 93405312000, 87178291200, 36933, 87091200], 'label': '6912.ia.72.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.br1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568176
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.w1', '36.bc1', '36.bb1', '36.bd1', '36.be1', '36.gt1'], 'contains': ['144.n1', '144.o1', '144.ie1', '144.if1', '144.du1', '144.dx1', '144.ei1', '144.kg1', '144.kh1', '216.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7656719, 9465, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.72.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568177
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.w1', '36.bf1', '36.bg1', '36.bh1', '36.bl1', '36.gq1'], 'contains': ['144.o1', '144.p1', '144.s1', '144.ej1', '144.el1', '144.fe1', '144.fk1', '216.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 36933, 119750400, 87124129], 'label': '6912.ia.72.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568178
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.t1', '36.y1', '36.bc1', '36.bj1', '36.bl1', '36.gu1'], 'contains': ['144.o1', '144.s1', '144.en1', '144.er1', '144.fm1', '216.s1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 43926348, 87178291200, 36933, 87124129], 'label': '6912.ia.72.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568179
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.s1', '36.x1', '36.bb1', '36.bh1', '36.bi1', '36.gu1'], 'contains': ['144.o1', '144.r1', '144.ih1', '144.il1', '144.em1', '144.eq1', '144.fl1', '144.kk1', '144.kq1', '216.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93405312000, 32929, 87178291200, 36933, 87124129, 83480268], 'label': '6912.ia.72.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568180
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.r1', '36.bj1', '36.bi1', '36.bk1', '36.bm1', '36.gt1'], 'contains': ['144.o1', '144.t1', '144.ep1', '144.es1', '144.fn1', '216.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 43909226, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.72.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568181
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.v1', '36.z1', '36.bb1', '36.bf1', '36.bj1', '36.gv1'], 'contains': ['144.o1', '144.ii1', '144.ij1', '144.et1', '144.ev1', '144.kl1', '144.km1', '216.u1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 19148, 36933, 40279680], 'label': '6912.ia.72.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568182
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.g1', '6.t1'], 'contains': ['24.j1', '24.dk1', '24.u1', '24.w1', '24.ee1', '36.g1', '36.be1', '48.k1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 2676, 87109068, 93405312000, 87124129, 32929, 7621226], 'label': '6912.ia.12.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.p1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568183
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.u1', '36.ba1', '36.bc1', '36.bg1', '36.bi1', '36.gv1'], 'contains': ['144.o1', '144.ij1', '144.eu1', '144.ey1', '144.kn1', '216.v1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 127390028, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.72.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.by1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568184
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.s1', '36.y1', '36.be1', '36.bg1', '36.bk1', '36.gw1'], 'contains': ['144.o1', '144.ik1', '144.ew1', '144.ez1', '144.ko1', '216.w1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 87100665, 83481548], 'label': '6912.ia.72.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.bz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568185
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.t1', '36.x1', '36.bd1', '36.bf1', '36.bm1', '36.gw1'], 'contains': ['144.o1', '144.im1', '144.ex1', '144.fa1', '144.kr1', '216.x1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 87100665, 119769548], 'label': '6912.ia.72.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ca1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568186
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.o1', '36.u1', '36.z1', '36.bd1', '36.bh1', '36.bk1'], 'contains': ['144.o1', '144.q1', '144.ig1', '144.in1', '144.eo1', '144.fb1', '144.fg1', '144.kj1', '144.ks1', '216.y1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 127370880, 40312609, 93405312000, 87178291200, 36933], 'label': '6912.ia.72.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cb1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568187
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.a1', '36.p1', '36.v1', '36.ba1', '36.be1', '36.bl1', '36.bm1'], 'contains': ['144.c1', '144.o1', '144.ig1', '144.ek1', '144.fc1', '144.ki1', '144.kp1', '216.z1'], 'core': '144.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40312609, 93405312000, 87178291200, 40297548, 36933, 40279680], 'label': '6912.ia.72.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.cc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568188
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.bh1', '36.gq1'], 'contains': ['144.p1', '144.q1', '144.r1', '144.fd1', '144.ff1', '144.fh1', '144.fo1', '216.ba1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 93405312000, 87178291200, 40297548, 36933, 119750400], 'label': '6912.ia.72.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568189
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.bh1', '36.gu1'], 'contains': ['144.q1', '144.s1', '144.r1', '144.fi1', '144.fj1', '144.fq1', '144.fp1', '216.bb1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43941409, 127388748, 93405312000, 87178291200, 40297548, 36933], 'label': '6912.ia.72.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bl1', 'old_label': '72.ce1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568190
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.be1', '36.gp1', '36.gq1'], 'contains': ['144.a1', '144.k1', '144.p1', '144.v1', '144.bq1', '144.fw1', '144.ge1', '144.pl1', '144.qm1', '216.hn1'], 'core': '144.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7620480, 127370880, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.72.ja1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.cf1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ja1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568191
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ej1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '24.bg1', '36.gp1', '36.gr1', '36.gs1'], 'contains': ['144.a1', '144.l1', '144.m1', '144.bp1', '144.br1', '144.fz1', '144.gi1', '144.pm1', '144.qn1', '216.ho1'], 'core': '144.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [127370880, 93405312000, 40280426, 87178291200, 36933, 40279680], 'label': '6912.ia.72.jb1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '72.cg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568192
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '24.bi1', '24.bj1', '36.gp1', '36.gr1', '36.gt1'], 'contains': ['144.a1', '144.n1', '144.t1', '144.bs1', '144.bt1', '144.gl1', '144.gp1', '144.pn1', '144.qo1', '216.hp1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127370880, 43909226, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.72.jc1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.ch1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568193
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.g1', '6.o1'], 'contains': ['24.j1', '24.x1', '24.y1', '36.h1', '36.bl1', '48.l1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43908480, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.q1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568194
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.in1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '36.a1', '36.gq1', '36.gs1', '36.gt1', '36.gu1', '36.gv1', '36.gw1'], 'contains': ['144.a1', '144.o1', '144.q1', '144.bu1', '144.bv1', '144.gw1', '144.gx1', '216.hq1'], 'core': '144.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [127370880, 40312609, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.72.jd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.ci1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 243568195
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '36.gq1', '36.gr1', '36.gu1'], 'contains': ['144.a1', '144.s1', '144.r1', '144.bx1', '144.bw1', '144.gy1', '144.gz1', '216.hr1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43941409, 127370880, 93405312000, 87178291200, 36933, 40279680], 'label': '6912.ia.72.je1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.je1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568196
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1'], 'contains': ['144.hu1', '144.hv1', '144.hx1', '144.hy1', '144.hz1', '144.ib1', '144.if1', '144.iu1', '144.iw1', '144.iy1', '144.jb1', '144.kt1', '144.kw1', '144.ln1', '144.lr1', '216.is1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 7656719, 93405312000, 87178291200, 36933, 87100665], 'label': '6912.ia.72.mj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '72.ck1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568197
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1', '36.k1', '36.jz1', '36.ka1'], 'contains': ['144.hu1', '144.hw1', '144.hz1', '144.ia1', '144.ie1', '144.iv1', '144.ix1', '144.jc1', '144.kv1', '144.kx1', '144.ls1', '216.it1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 7621226, 36933], 'label': '6912.ia.72.mk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mk1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568198
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.kb1', '36.kc1'], 'contains': ['144.hv1', '144.hw1', '144.ib1', '144.ic1', '144.ie1', '144.iz1', '144.ja1', '144.jd1', '144.lo1', '144.lp1', '144.lt1', '216.iu1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 36933, 83498639], 'label': '6912.ia.72.ml1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ml1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568199
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.jz1', '36.kb1'], 'contains': ['144.hw1', '144.hx1', '144.ig1', '144.ih1', '144.il1', '144.je1', '144.jg1', '144.jm1', '144.lu1', '144.lw1', '144.mc1', '216.iv1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87178291200, 36933, 87100665, 87124129], 'label': '6912.ia.72.mm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mm1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568200
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '36.m1', '36.ka1', '36.kb1'], 'contains': ['144.hw1', '144.ii1', '144.ik1', '144.jh1', '144.jj1', '144.lx1', '144.lz1', '216.iw1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 7654690, 36933], 'label': '6912.ia.72.mn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.co1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568201
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '36.jz1', '36.kc1'], 'contains': ['144.hw1', '144.ij1', '144.ik1', '144.ji1', '144.jk1', '144.ly1', '144.ma1', '216.ix1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87178291200, 36933, 83496610], 'label': '6912.ia.72.mo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 243568202
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1', '24.dg1', '36.p1', '36.ka1', '36.kc1'], 'contains': ['144.c1', '144.hw1', '144.ih1', '144.jf1', '144.jl1', '144.lv1', '144.mb1', '216.iy1'], 'core': '144.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 32929, 87178291200, 36933], 'label': '6912.ia.72.mp1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.cq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 243568203
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.v1', '36.jz1'], 'contains': ['144.ia1', '144.ig1', '144.ij1', '144.la1', '144.ld1', '144.my1', '144.nb1', '216.iz1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 87178291200, 36933, 746], 'label': '6912.ia.72.mq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mq1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568204
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.f1', '6.t1'], 'contains': ['24.j1', '24.z1', '24.ba1', '36.i1', '36.bm1', '48.m1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [87178291200, 36933, 43909226, 2676, 87109068, 93405312000, 87124129, 32929], 'label': '6912.ia.12.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.r1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568205
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1', '36.s1', '36.jz1', '36.ka1'], 'contains': ['144.ia1', '144.ih1', '144.ik1', '144.lc1', '144.le1', '144.na1', '144.nc1', '216.ja1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 83495329, 83496610], 'label': '6912.ia.72.mr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cs1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mr1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568206
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ms1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.di1', '36.v1', '36.ka1'], 'contains': ['144.c1', '144.ia1', '144.ii1', '144.lb1', '144.lf1', '144.mz1', '144.nd1', '216.jb1'], 'core': '144.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 36933, 746], 'label': '6912.ia.72.ms1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '72.ct1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ms1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568207
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.z1', '36.kb1'], 'contains': ['144.ic1', '144.ig1', '144.ii1', '144.mj1', '144.mn1', '144.nx1', '144.ob1', '216.jc1'], 'core': '576.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 87178291200, 36933, 127371626], 'label': '6912.ia.72.mt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cu1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mt1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568208
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '36.z1', '36.ba1'], 'contains': ['144.ic1', '144.ig1', '144.ij1', '144.mk1', '144.mo1', '144.ny1', '144.oc1', '216.jd1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [127388748, 9465, 93405312000, 40280426, 87178291200, 36933], 'label': '6912.ia.72.mu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bn1', 'old_label': '72.cv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mu1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568209
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.kb1', '36.kc1'], 'contains': ['144.ic1', '144.ih1', '144.ik1', '144.mm1', '144.mp1', '144.oa1', '144.od1', '216.je1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 7654690, 36933, 83495329], 'label': '6912.ia.72.mv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cw1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mv1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568210
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ei1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.v1', '36.ba1', '36.kc1'], 'contains': ['144.c1', '144.ic1', '144.ij1', '144.ml1', '144.mq1', '144.nz1', '144.oe1', '216.jf1'], 'core': '144.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 40280426, 87178291200, 36933], 'label': '6912.ia.72.mw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.cx1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mw1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568211
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1'], 'contains': ['144.id1', '144.il1', '144.im1', '144.mr1', '144.ms1', '144.of1', '144.og1', '216.jg1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7653409, 93405312000, 87178291200, 43942690, 36933, 87100665], 'label': '6912.ia.72.mx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '72.cy1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568212
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.my1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '36.jz1', '36.kb1'], 'contains': ['144.ie1', '144.ig1', '144.ik1', '144.ng1', '144.nk1', '144.oj1', '144.on1', '216.jh1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93405312000, 87178291200, 36933, 83463146, 87124129, 87109068], 'label': '6912.ia.72.my1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.cz1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.my1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568213
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.mz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '36.bb1', '36.ka1', '36.kb1'], 'contains': ['144.ie1', '144.ih1', '144.ii1', '144.ni1', '144.nl1', '144.ol1', '144.oo1', '216.ji1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 36933, 83498639, 83495329], 'label': '6912.ia.72.mz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.da1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.mz1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568214
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.na1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '36.jz1', '36.kc1'], 'contains': ['144.ie1', '144.ih1', '144.ij1', '144.nj1', '144.nm1', '144.om1', '144.op1', '216.jj1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 87178291200, 7621226, 36933, 83495329], 'label': '6912.ia.72.na1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.db1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.na1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568215
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1', '4.h1'], 'contains': ['24.f1', '24.g1', '24.h1', '24.i1', '24.be1', '24.bg1', '24.bh1', '24.k1', '24.l1', '24.n1', '24.o1', '24.bm1', '24.bn1', '24.ca1', '24.ce1', '24.eq1', '24.es1', '36.gd1', '36.gp1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 87178291200, 36933, 2676, 40279680], 'label': '6912.ia.12.bn1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '12.s1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 243568216
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1', '24.dm1', '24.dn1', '36.be1', '36.ka1', '36.kc1'], 'contains': ['144.c1', '144.ie1', '144.ik1', '144.nh1', '144.nn1', '144.ok1', '144.oq1', '216.jk1'], 'core': '144.c1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [9465, 93405312000, 32929, 87178291200, 7621226, 36933], 'label': '6912.ia.72.nb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.dc1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nb1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568217
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.nc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1', '36.bd1'], 'contains': ['144.if1', '144.im1', '144.in1', '144.no1', '144.np1', '144.or1', '144.os1', '216.jl1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [93405312000, 87178291200, 40297548, 36933, 87100665, 83463146], 'label': '6912.ia.72.nc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '72.dd1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.nc1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 243568218
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '24.k1', '36.gd1'], 'contains': ['144.u1', '144.x1', '144.be1', '144.bk1', '144.bn1', '144.cl1', '144.dy1', '144.qp1', '216.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87218570880, 30938, 36933, 87091200, 83468087], 'label': '6912.ia.72.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.de1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568219
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '24.l1', '36.gd1'], 'contains': ['144.u1', '144.z1', '144.bb1', '144.bm1', '144.bo1', '144.dg1', '144.do1', '144.qq1', '216.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 36933, 2676, 87091200], 'label': '6912.ia.72.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.gd1', 'old_label': '72.df1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 243568220
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.gp1', '36.bo1', '36.bp1'], 'contains': ['144.v1', '144.w1', '144.bd1', '144.bp1', '144.bs1', '144.ce1', '144.ds1', '144.qr1', '216.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 87218570880, 93405312000, 36933, 87091200, 83468087], 'label': '6912.ia.72.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dg1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568221
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.gp1', '36.bo1', '36.bq1'], 'contains': ['144.v1', '144.y1', '144.ba1', '144.br1', '144.bt1', '144.da1', '144.dk1', '144.qs1', '216.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 87218570880, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.72.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dh1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568222
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gq1', '36.bp1', '36.bq1', '36.bt1', '36.br1', '36.bs1', '36.bu1'], 'contains': ['144.v1', '144.bg1', '144.bj1', '144.bu1', '144.bw1', '144.el1', '144.fo1', '216.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 87305662080, 93405312000, 32929, 36933, 87124129], 'label': '6912.ia.72.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.di1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568223
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.gq1', '36.bo1', '36.bt1'], 'contains': ['144.v1', '144.bi1', '144.bh1', '144.bv1', '144.bx1', '144.fk1', '144.fh1', '216.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 127388748, 87305662080, 93405312000, 40297548, 36933], 'label': '6912.ia.72.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dj1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568224
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.bo1', '36.gx1'], 'contains': ['144.w1', '144.ba1', '144.bi1', '144.bz1', '144.cc1', '144.dh1', '144.du1', '144.iv1', '144.iw1', '144.iy1', '144.iz1', '216.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 87265391865, 36933, 87091200, 83468087], 'label': '6912.ia.72.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dk1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 243568225
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bp1', '36.gx1'], 'contains': ['144.w1', '144.bd1', '144.bj1', '144.cb1', '144.cg1', '144.dt1', '144.dw1', '216.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 93405312000, 36933, 87091200, 83468087, 87305671545], 'label': '6912.ia.72.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dl1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568226
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '6.p1'], 'contains': ['24.a1', '24.bf1', '24.bi1', '24.bo1', '24.bq1', '24.bv1', '24.cf1', '24.et1', '36.ge1', '36.gp1', '48.cu1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7620480, 127370880, 43909226, 93405312000, 87178291200, 47537280, 36933, 40279680], 'label': '6912.ia.12.bo1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1', 'old_label': '12.t1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 243568227
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bo1', '36.gy1'], 'contains': ['144.w1', '144.y1', '144.bh1', '144.cf1', '144.ch1', '144.cy1', '144.dv1', '216.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127380345, 43909226, 93405312000, 36933, 87091200], 'label': '6912.ia.72.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dm1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 243568228
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.bp1', '36.bv1', '36.bw1', '36.bx1', '36.by1', '36.gy1'], 'contains': ['144.w1', '144.bg1', '144.ca1', '144.ci1', '144.dx1', '144.iu1', '144.ix1', '144.ja1', '216.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 7656719, 9465, 93405312000, 36933, 87100665], 'label': '6912.ia.72.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dn1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 243568229
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bq1', '36.gx1'], 'contains': ['144.y1', '144.ba1', '144.bj1', '144.cw1', '144.db1', '144.dm1', '144.eh1', '216.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 36933, 87091200, 87305671545], 'label': '6912.ia.72.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.do1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568230
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.bo1', '36.gx1'], 'contains': ['144.y1', '144.bd1', '144.bi1', '144.cz1', '144.dd1', '144.ee1', '144.fn1', '216.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 43909226, 93405312000, 87265391865, 36933, 87091200], 'label': '6912.ia.72.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dp1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568231
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.bq1', '36.ca1', '36.cb1', '36.cc1', '36.cd1', '36.gy1'], 'contains': ['144.y1', '144.bg1', '144.dc1', '144.de1', '144.ep1', '216.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 43909226, 93405312000, 36933, 87100665], 'label': '6912.ia.72.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dq1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 243568232
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '36.bo1', '36.gz1'], 'contains': ['144.ba1', '144.bd1', '144.bh1', '144.dl1', '144.dq1', '144.ea1', '144.eg1', '216.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7620480, 127380345, 93405312000, 87222200426, 36933, 87091200], 'label': '6912.ia.72.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bj1', 'old_label': '72.dr1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 243568233
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.bq1', '36.cf1', '36.cg1', '36.ch1', '36.ci1', '36.gz1'], 'contains': ['144.ba1', '144.bg1', '144.di1', '144.dr1', '144.ei1', '144.jb1', '144.jc1', '144.jd1', '216.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 87185947919, 93405312000, 36933, 87100665], 'label': '6912.ia.72.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.ds1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568234
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.bp1', '36.cl1', '36.cm1', '36.cn1', '36.co1', '36.gz1'], 'contains': ['144.bd1', '144.bg1', '144.ed1', '144.ef1', '144.es1', '216.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 9465, 93405312000, 87222200426, 36933, 87100665], 'label': '6912.ia.72.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dt1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}
  • id: 243568235
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '36.bt1', '36.bv1', '36.ca1', '36.cf1', '36.cl1', '36.ha1'], 'contains': ['144.bg1', '144.bi1', '144.ek1', '144.eq1', '144.fl1', '144.jf1', '144.jg1', '144.jm1', '216.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 36933, 87265400268, 87124129], 'label': '6912.ia.72.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.du1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 243568236
    {'ambient': '6912.ia', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.bu1', '36.bw1', '36.cb1', '36.cg1', '36.cm1', '36.ha1'], 'contains': ['144.bg1', '144.bj1', '144.eo1', '144.er1', '144.fp1', '216.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7620480, 93405312000, 32929, 87218588748, 36933, 87124129], 'label': '6912.ia.72.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '72.dv1', 'projective_image': '3456.jo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1', 'subgroup_fusion': None, 'weyl_group': '192.1514'}